DOT/FRA/ORD-13/17 Final Report | September 2023

Detailed Puncture Analyses of Tank Cars - Analysis of 

Different Impactor Threats and Impact Conditions 

Revision 1

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4. TITLE AND SUBTITLE

Detailed Puncture Analyses of Tank Cars - Analysis of Different Impactor Threats and 

Impact Conditions – Revision 1

5a. CONTRACT NUMBER

693JJ622C000002

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Steven W Kirkpatrick: ORCID 0000-0001-9590-7980

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

Applied Research Associates

95 First Street, Suite 100

Los Altos, CA 94022

8. PERFORMING ORGANIZATION

REPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

U.S. Department of Transportation

Federal Railroad Administration

Office of Railroad Policy and Development

Office of Research, Development, and Technology

Washington, DC 20590

10. SPONSOR/MONITOR'S ACRONYM(S)

11. SPONSOR/MONITOR'S REPORT

NUMBER(S)

DOT/FRA/ORD-13/17

12. DISTRIBUTION/AVAILABILITY STATEMENT

This document is available to the public through the FRA website. 

13. SUPPLEMENTARY NOTES

COR: Francisco González, III

14. ABSTRACT

This report describes a research program to improve the safety and security of railroad tank cars. The approach used in the research and 

development program was to apply a tank impact and puncture prediction capability using detailed finite element analyses (FEA). The FEA 

capability was developed and validated previously in the NGRTC program. The analysis methodologies apply advanced damage and failure 

models that were validated by series of material tests under various loading conditions. In this study, the analyses were applied to investigate 

the tank puncture behaviors for a wide range of impact conditions. 

15. SUBJECT TERMS

Tank Car, Impact, Puncture, Crash, Derailment, Hazmat Safety

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

ABSTRACT

18. NUMBER

OF

PAGES

273

19a. NAME OF RESPONSIBLE PERSON

a. REPORT b. ABSTRACT c. THIS PAGE

19b. TELEPHONE NUMBER (Include area code)

Standard Form 298 (Rev. 8/98)

Prescribed by ANSI Std. Z39.18
ii

METRIC/ENGLISH CONVERSION FACTORS

ENGLISH TO METRIC METRIC TO ENGLISH

LENGTH (APPROXIMATE) LENGTH (APPROXIMATE) 

1 inch (in) = 2.5 centimeters (cm) 1 millimeter (mm) = 0.04 inch (in)

1 foot (ft) = 30 centimeters (cm) 1 centimeter (cm) = 0.4 inch (in)

1 yard (yd) = 0.9 meter (m) 1 meter (m) = 3.3 feet (ft)

1 mile (mi) = 1.6 kilometers (km) 1 meter (m) = 1.1 yards (yd)

1 kilometer (km) = 0.6 mile (mi)

AREA (APPROXIMATE) AREA (APPROXIMATE) 

1 square inch (sq in, in2) = 6.5 square centimeters (cm2) 1 square centimeter (cm2) = 0.16 square inch (sq in, in2) 

1 square foot (sq ft, ft2) = 0.09 square meter (m2) 1 square meter (m2) = 1.2 square yards (sq yd, yd2)

1 square yard (sq yd, yd2) = 0.8 square meter (m2) 1 square kilometer (km2) = 0.4 square mile (sq mi, mi2)

1 square mile (sq mi, mi2) = 2.6 square kilometers (km2) 10,000 square meters (m2) = 1 hectare (ha) = 2.5 acres

1 acre = 0.4 hectare (he) = 4,000 square meters (m2) 

MASS - WEIGHT (APPROXIMATE) MASS - WEIGHT (APPROXIMATE) 

1 ounce (oz) = 28 grams (gm) 1 gram (gm) = 0.036 ounce (oz)

1 pound (lb) = 0.45 kilogram (kg) 1 kilogram (kg) = 2.2 pounds (lb)

1 short ton = 2,000 pounds (lb) = 0.9 tonne (t) 1 tonne (t) =

=

1,000 kilograms (kg)

1.1 short tons

VOLUME (APPROXIMATE) VOLUME (APPROXIMATE) 

1 teaspoon (tsp) = 5 milliliters (ml) 1 milliliter (ml) = 0.03 fluid ounce (fl oz)

1 tablespoon (tbsp) = 15 milliliters (ml) 1 liter (l) = 2.1 pints (pt)

1 fluid ounce (fl oz) = 30 milliliters (ml) 1 liter (l) = 1.06 quarts (qt)

1 cup (c) = 0.24 liter (l) 1 liter (l) = 0.26 gallon (gal)

1 pint (pt) = 0.47 liter (l)

1 quart (qt) = 0.96 liter (l)

1 gallon (gal) = 3.8 liters (l)

1 cubic foot (cu ft, ft3) = 0.03 cubic meter (m3) 1 cubic meter (m3) = 36 cubic feet (cu ft, ft3) 

1 cubic yard (cu yd, yd3) = 0.76 cubic meter (m3) 1 cubic meter (m3) = 1.3 cubic yards (cu yd, yd3)

TEMPERATURE (EXACT) TEMPERATURE (EXACT) 

[(x-32)(5/9)] °F = y °C [(9/5) y + 32] °C = x °F

QUICK INCH - CENTIMETER LENGTH CONVERSION

0 1 2 3 4 5

Inches

Centimeters 0 1 2 3 4 5 6 987 1110 1312

QUICK FAHRENHEIT - CELSIUS TEMPERATURE CONVERSIO

 -40° -22° -4° 14° 32° 50° 68° 86° 104° 122° 140° 158° 176° 194° 212°

 

°F

 °C -40° -30° -20° -10° 0° 10° 20° 30° 40° 50° 60° 70° 80° 90° 100°

For more exact and or other conversion factors, see NIST Miscellaneous Publication 286, Units of Weights and 

Measures. Price $2.50 SD Catalog No. C13 10286 Updated 6/17/98
iii

Contents

Acknowledgements ................................................................................................................ xvii

Executive Summary ................................................................................................................... 1

1. Introduction .......................................................................................................................17

1.1 Background .................................................................................................................. 17

1.2 Material Damage and Failure Behaviors....................................................................... 22

1.3 Tank Car Puncture Modeling ....................................................................................... 22

2. Material Constitutive and Damage Models.........................................................................25

2.1 Introduction ................................................................................................................. 25

2.2 TC128B Material Properties......................................................................................... 25

2.3 Bao-Wierzbicki Failure Surface ................................................................................... 29

2.4 Material Characterization Testing and Analyses........................................................... 31

2.4.1 Tensile Tests and Analyses..................................................................................... 31

2.4.2 Notched Round Bar Tensile Tests and Analyses..................................................... 33

2.4.3 Tensile-Shear Tests and Analyses........................................................................... 34

2.4.4 Punch Tests and Analyses ...................................................................................... 36

2.5 Cryogenic 304 Stainless Steel Material Properties........................................................ 39

2.5.1 Constitutive Model for A240 304 SS at LNG Temperature..................................... 40

2.5.2 Constitutive Model for A240 304 SS at Liquid Nitrogen Temperature.................... 45

3. Analysis of Different Size and Shape Impactors.................................................................48

3.1 Introduction and Background ....................................................................................... 48

3.1.1 Puncture Analysis Methodologies........................................................................... 48

3.2 Side Impact Analysis of Different Size and Shape Impactors........................................ 53

3.2.1 Effects of Impactor Size and Shape ........................................................................ 55

3.2.2 Definition of the Impactor Characteristic Size ........................................................ 62

3.2.3 Analysis of Impactor Edge Sharpness..................................................................... 64

3.2.4 Analysis of Complex Impactor Shapes................................................................... 67

3.2.5 Analysis of Impactor Orientation Effects................................................................ 77

3.3 Head Impact Analysis of Different Size and Shape Impactors...................................... 82

3.3.1 Effects of Impactor Size and Shape ........................................................................ 82

3.3.2 Analysis of Complex Impactor Shapes................................................................... 86

3.3.3 Analysis of Offset Head Impact Location Effects................................................... 93

3.4 Analysis of Impact Speed Effects................................................................................. 95

3.4.1 Analysis of Impact Speed for Side Impacts............................................................. 95

3.4.2 Analysis of Impact Speed for Head Impacts ........................................................... 99

3.5 Analysis of Tank and Lading Temperature Effects....................................................... 99
iv

4. Analysis of General Impact Conditions............................................................................ 103

4.1 Introduction ............................................................................................................... 103

4.2 Oblique Impacts......................................................................................................... 103

4.3 Impact Boundary Condition Effects ........................................................................... 109

4.3.1 Side Impact Constraint Effects ............................................................................. 109

4.4 Lading Response Effects............................................................................................ 117

4.4.1 Lading Effects for Side Impacts............................................................................ 117

4.4.2 Lading Effects for Head Impacts.......................................................................... 123

4.5 Head Impact Test Configuration................................................................................. 126

4.5.1 Trailing Mass Effects for the Impactor ................................................................. 129

4.5.2 Summary of the Head Impact Test Evaluation...................................................... 132

4.6 Analysis of Offset Side Impact Effects....................................................................... 133

4.6.1 Analysis of Vertical Offset Side Impacts.............................................................. 133

4.6.2 Analysis of Longitudinal Offset Side Impacts....................................................... 136

5. Impact Analyses on Other Tank Car Designs................................................................... 140

5.1 Introduction and Background ..................................................................................... 140

5.2 Chlorine Tank Cars.................................................................................................... 141

5.2.1 Side Impacts of Chlorine Tank Cars..................................................................... 141

5.2.2 Head Impacts of Chlorine Tank Cars.................................................................... 146

5.3 Ethylene Oxide Tank Cars.......................................................................................... 149

5.3.1 Normal side Impacts of EO Tank Cars.................................................................. 149

5.3.2 Offset Impacts of EO Tank Cars........................................................................... 150

5.3.3 Oblique Impacts of EO Tank Cars........................................................................ 152

5.3.4 Summary of EO Tank Shell Puncture Performance............................................... 153

5.3.5 Head Impacts of EO Tank Cars............................................................................ 155

5.4 Anhydrous Ammonia Tank Cars................................................................................ 156

5.4.1 Normal side Impacts of AA Tank Cars................................................................. 157

5.4.2 Oblique Impacts of AA Tank Cars........................................................................ 158

5.4.3 Summary of AA Tank Shell Puncture Performance .............................................. 159

5.4.4 Head Impacts of AA Tank Cars............................................................................ 160

5.5 Comparison of the Various Pressure tank Car designs................................................ 162

5.6 DOT Class 111 tank cars............................................................................................ 164

5.6.1 Effects of Outage Volume .................................................................................... 166

5.6.2 Analyses of Different General Purpose Tank Designs........................................... 172

5.6.3 Offset Impact Analyses ........................................................................................ 179

5.6.4 Head Impacts of General-Purpose Tank Cars........................................................ 180
v 

5.6.5 Summary of Analyses for General Purpose Tank Cars.......................................... 182

5.7 DOT Class 113 Cryogenic LNG tank cars.................................................................. 184

5.7.1 Summary of Test Results...................................................................................... 184

5.7.2 Model Validation ................................................................................................. 186

5.7.3 DOT Class 113 LNG Tank Model........................................................................ 189

5.7.4 Baseline DOT Class 113 LNG Tank Analyses...................................................... 194

5.7.5 Modified DOT Class 113 LNG Tank Analyses..................................................... 198

5.7.6 Head Impacts of DOT Class 113 LNG Tank Cars................................................. 201

6. Analytical Models for Tank Car Impacts.......................................................................... 204

6.1 Introduction ............................................................................................................... 204

6.2 Head Impact Analyses................................................................................................ 204

6.2.1 Head Impact Analysis Algorithm.......................................................................... 204

6.3 Side Impact Analyses................................................................................................. 209

6.3.1 Supporting FE Tank Analyses.............................................................................. 210

6.3.2 Side Impact Analysis Algorithm........................................................................... 218

6.4 Development of the Characteristic Puncture Force ..................................................... 223

7. Analysis of Real-World Threats....................................................................................... 231

7.1 Introduction and Background ..................................................................................... 231

7.2 Protection System Design........................................................................................... 231

7.3 Side Impact Puncture Analyses.................................................................................. 234

8. Conclusions ..................................................................................................................... 241

9. References....................................................................................................................... 244

Appendix A. Tank Head Puncture Resistance Performance Standards..................................... 249

Abbreviations and Acronyms.................................................................................................. 251
vi 

Illustrations

Figure 1. Correlation of side impact puncture forces with ram characteristic size. .......................1

Figure 2. Correlation of side impact puncture energies with ram characteristic size. ....................2

Figure 3. Puncture forces for the 12x12 inch impactor at various orientations..............................3

Figure 4. Comparison of puncture forces for normal and oblique impacts....................................4

Figure 5. Comparison of puncture energies for normal and oblique impacts. ...............................4

Figure 6. Comparison of the calculated head and side impact puncture forces. ............................5

Figure 7. Comparison of the calculated head and side impact puncture energies..........................5

Figure 8. The effects of constraint conditions for the 15 mph constant velocity impacts. .............6

Figure 9. The effects of tank motion BCs on head impact response. ............................................8

Figure 10. Calculated longitudinal velocity distribution in the SPH lading. .................................9

Figure 11. The effects of lading on unconstrained head impact response. ....................................9

Figure 12. Normalized side impact puncture energies at 105o F................................................. 10

Figure 15. Comparison of the 1D model and FEA of head impact behaviors. ............................ 12

Figure 16. Idealized schematic of the side impact spring mass model. ....................................... 13

Figure 17. Comparison of the FEA and impact algorithm for different speed impacts................ 14

Figure 18. Initial set of tank puncture forces under various impact conditions. .......................... 15

Figure 19. Correlation of characteristic puncture forces for various impact conditions............... 15

Figure 20. Number of Rail Accidents Releasing Hazardous Materials (FRA, 2023)................... 18

Figure 21. A graphical illustration of the initial tank car safety research areas. .......................... 19

Figure 22. Summary of tank car safety research including ATCCRP Projects............................ 21

Figure 23. Detailed FE simulation evaluation for the Tiskilwa, IL derailment............................ 21

Figure 24. Calculated puncture behavior of a head and head shield............................................ 23

Figure 25. Calculated puncture forces as a function of system thickness.................................... 23

Figure 26. Loading and failure mechanism for the tank impact and puncture............................. 24

Figure 27. Material testing data for different TC128B materials. ............................................... 26

Figure 28. Comparison of engineering and true stress-strain data for TC128B........................... 27

Figure 29. Tabular true stress curve developed for the TC128B constitutive model. .................. 28

Figure 30. Comparison of the measured and calculated TC128B tensile test.............................. 28

Figure 31. Local damage criterion for tensile ductile fracture analyses. ..................................... 30

Figure 32. Bao-Wierzbicki failure surface and tests used for model calibration. ........................ 31

Figure 33. Dimensions of the specimen used in tensile testing................................................... 32
vii 

Figure 34. Necking behavior observed in the TC128B round bar specimens.............................. 32

Figure 35. Validation of the tensile test behavior for TC128B. .................................................. 33

Figure 36. Test setup for the TC128B notched round bar specimens.......................................... 34

Figure 37. Validation of the notched round bar test behavior for TC128B. ................................ 34

Figure 38. Specimen geometries for the combined tensile shear tests......................................... 35

Figure 39. Photograph of the combined tensile shear test configuration..................................... 35

Figure 40. Analysis of the specimen behavior in the pure shear orientation. .............................. 36

Figure 41. Validation of the combined tensile shear test behavior for TC128B. ......................... 36

Figure 42. Simulation of the punch test on the thin TC128B plate material................................ 37

Figure 43. Punch test failure mode for the thin TC128B plate material. ..................................... 38

Figure 44. Simulation of the punch test on the thin TC128B plate material................................ 38

Figure 45. Force-deflection curves for three punch test configurations on TC128B. .................. 39

Figure 46. Comparison of the calculated and measured punch test plate profile. ........................ 39

Figure 57. Tank model and impact zone mesh used for side impact puncture analyses............... 49

Figure 58. Tank head model and impact zone mesh used for the head puncture analyses. .......... 49

Figure 59. Calculated tank car impact behavior using two different lading models. ................... 50

Figure 60. Pressure-volume relationship used for the tank control volume (10.6% outage). ....... 51

Figure 61. Effect of variable internal pressure on 500 lb tank impact response. ......................... 51

Figure 62. Calculated internal pressure variations in the 500 lb tank impact analyses. ............... 52

Figure 63. Simplified tank model analysis with Bao-Wierzbicki failure assessment................... 52

Figure 64. Comparison of the calculated and measured Test 2 impact and puncture behavior. ... 53

Figure 65. Detailed impact and puncture sequence for a 600 lb chlorine car. ............................. 54

Figure 66. Calculated puncture initiation and fracture progression............................................. 55

Figure 67. Calculated energy balance for the 600 lb chlorine tank car impact (R10F). ............... 55

Figure 68. Tank model and impact zone mesh used for the 12x12 inch impactor. ...................... 56

Figure 69. Models of the different size square impactors. .......................................................... 57

Figure 70. Updated 600 lb tank impact analysis with different size impactors............................ 57

Figure 71. Puncture forces for the 600 lb tank impacts with different size impactors. ................ 58

Figure 72. Calculated puncture behaviors (3x3 and 12x12 inch Impactors)................................ 58

Figure 74. Puncture forces for the 600 lb tank impacts with different size impactors. ................ 59

Figure 75. Calculated puncture behaviors (3x3 and 12x12 inch Impactors)................................ 60

Figure 76. Models of the different size round impactors. ........................................................... 61
viii

Figure 77. Puncture forces for the 600 lb tank impact analyses with different size and shape 

impactors........................................................................................................................... 61

Figure 78. Calculated puncture behaviors for different size round impactors. ............................ 62

Figure 79. Correlation of the puncture forces with ram characteristic size.................................. 64

Figure 80. Correlation of the puncture energies with ram characteristic size. ............................. 64

Figure 81. Calculated force-deflection behaviors for the impactor edge radii evaluations. ......... 66

Figure 82. Calculated puncture behavior for the 3x12impactor with 0.5- and 0.1-inch edge radii.

.......................................................................................................................................... 67

Figure 83. Model for the rail section impactor........................................................................... 68

Figure 84. Geometry for the rail section impactor...................................................................... 69

Figure 85. Calculated side impact puncture behavior for the rail section impactor. .................... 70

Figure 86. Puncture forces for the 600 lb tank impact analyses with the rail impactor................ 71

Figure 87. Model for the coupler head impactor. ....................................................................... 71

Figure 88. Calculated puncture behavior for the coupler head normal impact. ........................... 73

Figure 89. Calculated force-deflection behavior for the coupler head normal impact. ................ 74

Figure 90. Calculated puncture behavior for the coupler head 15-degree rotation impact........... 74

Figure 91. Calculated force-deflection behavior for the coupler 15-degree rotation impact. ....... 75

Figure 92. Calculated puncture behavior for the coupler -15-degree rotation impact.................. 76

Figure 93. Calculated force-deflection behavior for the coupler -15-degree rotation impact....... 77

Figure 94. Puncture forces for the 600 lb tank impact analyses with the coupler head impactor. 77

Figure 95. Example impactor orientation analyses performed for side impacts. ......................... 78

Figure 96. Calculated force-deflection behaviors for the 12x12 inch impactor and various levels 

of yaw rotations................................................................................................................. 78

Figure 97. Puncture forces for the 12x12 inch impactor at various orientations. ......................... 80

Figure 98. Puncture behavior for the 12x12 inch impactor with face, edge, and corner impacts. 81

Figure 99. Analysis of the tank head puncture behavior for the 6x6 inch impactor..................... 83

Figure 100. Calculated head impact force-deflection behaviors for the square impactors. .......... 84

Figure 101. Calculated head impact puncture forces for various impactors. ............................... 84

Figure 102. Calculated head puncture behaviors for the 3x12 and 12x3 impactors..................... 85

Figure 103. Comparison of the calculated head and side impact puncture forces........................ 86

Figure 104. Comparison of the calculated head and side impact puncture energies. ................... 86

Figure 105. Analysis of the 11-mph rail section impact behavior on the constrained head. ........ 87

Figure 106. Calculated head impact puncture behavior for the rail section impactor. ................. 88
ix

Figure 107. Calculated head puncture impact response for the rail section impactor. ................. 88

Figure 108. Calculated head impact puncture forces for various impactors. ............................... 89

Figure 109. Calculated head puncture behavior for the upside-down rail impactor..................... 89

Figure 110. Calculated head impact response for the rail section impactors. .............................. 90

Figure 111. Analysis of the 18-mph coupler impact behavior on the constrained head............... 90

Figure 112. Calculated damage for the 18-mph coupler impact on the constrained head. ........... 91

Figure 113. Calculated damage for the 25-mph coupler impact on the constrained head. ........... 92

Figure 114. Calculated head puncture impact response for the rigid coupler impactor. .............. 93

Figure 115. Calculated head impact puncture forces for various impactors. ............................... 93

Figure 116. Impact scenarios used in the vertical offset impact analyses.................................... 94

Figure 117. Calculated force-deflection behaviors for variable offset head impacts. .................. 95

Figure 118. Comparison of side impact behaviors at different impact speeds............................. 96

Figure 119. Comparison of side impact puncture forces at different impact speeds.................... 96

Figure 120. Comparison of side impact puncture energies at different impact speeds................. 97

Figure 121. Comparison of the tank side loading response at different speeds. .......................... 97

Figure 122. Comparison of the tank side loading response at different speeds. .......................... 98

Figure 123. Comparison of the tank side loading response at different speeds. .......................... 98

Figure 124. Comparison of Head impact behaviors at different impact speeds........................... 99

Figure 125. Physical properties of chlorine as a function of temperature.................................. 100

Figure 126. Pressure-volume relationships for the chlorine tank car at 78o and 105o F............. 101

Figure 127. Comparison of side impact puncture forces at 78o and 105o F............................... 101

Figure 128. Comparison of the side impact puncture energies at 78o and 105o F...................... 102

Figure 129. Normalized side impact puncture energies at 105o F. ............................................ 102

Figure 130. Various oblique impact conditions investigated for side impacts........................... 103

Figure 131. The effects of impact obliquity on the tank impact and puncture response. ........... 104

Figure 132. Oblique impact damage development and puncture behavior for side impacts. ..... 105

Figure 133. The effects of impact obliquity on the tank impact response and puncture. ........... 106

Figure 134. Effect of impactor angle on oblique impact response for side impacts................... 107

Figure 135. The effects of impact obliquity on the tank impact response and puncture. ........... 107

Figure 136. Comparison of puncture forces for normal and oblique impacts............................ 108

Figure 137. Comparison of puncture energies for normal and oblique impacts. ....................... 108

Figure 138. Various tank motion constraint BCs for side impacts............................................ 109
x 

Figure 139. The effects of constraint conditions for a 25-mph impact and 9.55-inch-diameter 

impactor, with differing tank weights. ............................................................................. 110

Figure 140. The effects of constraint conditions for the 15 mph constant velocity impacts....... 111

Figure 141. The effects of impact speed on the highly constrained side impacts. ..................... 112

Figure 142. Calculated response for the symmetric tank side impact scenario.......................... 113

Figure 143. The effects of constraint BCs on the side impact response. ................................... 114

Figure 144. The effects of constraint BCs on the side impact response. ................................... 114

Figure 145. Various tank motion constraint BCs for side impacts............................................ 115

Figure 146. The effects of BC restraint on head impact response (18 mph impacts)................ 116

Figure 147. The effects of BC restraint on head impact response (25 mph coupler impacts). .. 117

Figure 148. Updated model generated for a 105J500W pressure tank car................................. 118

Figure 149. Calculated Test 1 impact response with cutaway showing lading.......................... 118

Figure 150. Comparison of the measured and predicted Test 1 force-deflection curves............ 119

Figure 151. Various model support BCs for a 105J500W pressure tank car. ............................ 120

Figure 152. Calculated tank car impact behavior using three different support BCs. ................ 121

(a) Before impact (time=0.0 s) (b) Near first load peak (time=0.10 s) ................................... 122

Figure 153. Calculated side impact response with SPH lading model. ..................................... 122

Figure 154. Calculated tank car impact behavior using two different lading models. ............... 123

Figure 155. Calculated head impact response with SPH lading model. .................................... 124

Figure 156. Calculated tank car head impact behavior using different lading models............... 124

Figure 157. Calculated longitudinal velocity distribution in the SPH lading............................. 125

Figure 158. Calculated tank car head impact behavior using different lading models............... 126

Figure 159. Tank head impact analysis model geometry.......................................................... 126

Figure 160. Model of the 263,000 lb coupler impactor sled. .................................................... 127

Figure 161. Force-deflection characteristics used for the energy absorbing raft gear................ 128

Figure 162. Comparison of 25 mph coupler impact and puncture behaviors............................. 128

Figure 163. Momentum transfer for the tank car head impact analysis..................................... 130

Figure 164. Velocity histories for the 1.3X lading head impact analysis. ................................. 130

Figure 165. Calculated impact behavior using the 1.3X lading model...................................... 131

Figure 166. Velocity histories for the smeared full lading head impact analysis....................... 131

Figure 167. Calculated head impact behavior using the smeared full lading models................. 132

Figure 168. Impact scenarios used in the vertical offset impact analyses.................................. 134

Figure 169. Comparison of the calculated side impact behavior with vertical offsets. .............. 134
xi 

Figure 170. Calculated puncture behavior for the 25-inch vertical offset side impact............... 135

Figure 171. Calculated puncture forces for the various vertical offset side impacts.................. 136

Figure 172. Calculated puncture energies for the various vertical offset side impacts............... 136

Figure 173. Various impact locations investigated for unconstrained side impacts................... 137

Figure 174. The effects of longitudinal offsets on unconstrained side impact behavior. ........... 137

Figure 175. Longitudinal offset impact locations investigated for constrained side impacts. .... 138

Figure 176. Offset impact effects on a constrained tank, constant 15 mph impact.................... 139

Figure 177. Offset impact effects on a constrained tank, 25 mph initial velocity impact........... 139

Figure 178. Comparison of physical properties of common pressure tank car commodities. .... 140

Figure 179. Tank pressure-volume relationships for various commodities (10.6% outage). ..... 141

Figure 180. Puncture force comparisons for the 105J500 and 105J600 tank cars...................... 144

Figure 181. Puncture energy comparisons for the 105J500 and 105J600 tank cars................... 144

Figure 182. Comparison of the offset impact puncture energies for the 105J500 and 105J600 

tank cars. ......................................................................................................................... 145

Figure 183. Comparison of the 45-degree oblique impact puncture energies for the 105J500 and

105J600 tank cars. ........................................................................................................... 145

Figure 184. Normalized puncture energy summary for the 105J600 tank cars.......................... 146

Figure 189. Calculated baseline EO tank puncture forces for various size and shape impactors.

........................................................................................................................................ 150

Figure 190. Calculated baseline EO tank puncture energies for various size and shape impactors.

........................................................................................................................................ 150

Figure 191. Calculated puncture forces for the various vertical offset side impacts.................. 151

Figure 192. Calculated puncture energies for the various vertical offset side impacts............... 151

Figure 193. Impact scenario for the 45-degree oblique side impact analyses............................ 152

Figure 194. Comparison of puncture forces for normal and oblique impacts............................ 152

Figure 195. Comparison of puncture energies for normal and oblique impacts. ....................... 153

Figure 196. Comparison of relative puncture performance of the baseline EO tank designs. .... 154

Figure 197. Comparison of relative puncture performance of EO and chlorine tank designs. ... 154

Figure 200. Calculated baseline AA tank puncture forces for various size and shape impactors.

........................................................................................................................................ 157

Figure 201. Calculated baseline AA tank puncture energies for various size and shape impactors.

........................................................................................................................................ 158

Figure 202. Comparison of puncture forces for normal and oblique impacts............................ 158

Figure 203. Comparison of puncture energies for normal and oblique impacts. ....................... 159
xii 

Figure 204. Comparison of relative puncture performance of AA and chlorine tank designs.... 160

Figure 207. Comparison of relative puncture performance of various tank cars. ...................... 162

Figure 210. Model of a 23,000-gallon DOT-111A100W tank for analysis of outage volume 

effects.............................................................................................................................. 166

Figure 211. Control volume pressure curves for various outages between 1 and 18 percent. .... 167

Figure 212. Calculated impact and puncture behaviors for different outage volumes. .............. 168

Figure 213. Force-deflection curves and puncture energies for different outage volumes......... 169

Figure 214. Control volume pressures for impacts with different outage volumes.................... 170

Figure 215. Effect of the outage volume on the puncture energy in side impacts...................... 171

Figure 216. Force-deflection curve and impact energy dissipation for an empty tank............... 171

Figure 217. Side impact damage distribution for 1% and 18% outage volumes........................ 172

Figure 218. Correlation of the side impact puncture forces with the impactor characteristic size.

........................................................................................................................................ 172

Figure 219. Comparison of the normalized side impact puncture forces................................... 173

Figure 220. Correlation of the side impact puncture energies with the ram face characteristic size.

........................................................................................................................................ 174

Figure 221. Calculated force-deflection curves for the 105J600 and 111A100W3 tank cars..... 175

Figure 222. Calculated pressure-deflection curves for the 105J600 and 111A100W3 tank cars.

........................................................................................................................................ 176

Figure 223. Comparison of calculated puncture forces for 1% and 3% outage. ........................ 177

Figure 224. Comparison of calculated puncture energies for 1% and 3% outage...................... 178

Figure 225. Comparison of force-deflection characteristics for 1% and 3% outage. ................. 178

Figure 226. Comparison of calculated tank pressures for analyses with 1% and 3% outage. .... 179

Figure 227. Calculated puncture forces for the various vertical offset side impacts.................. 179

Figure 228. Calculated puncture energies for the various vertical offset side impacts............... 180

Figure 260. The effects of BC restraint on head impact response............................................. 205

Figure 261. Comparison of the 1D model and FEA predictions for tank impact forces (18 mph 

impacts)........................................................................................................................... 206

Figure 262. Comparison of the FEA analyses with unloading behaviors.................................. 207

Figure 263. Comparison of the 1D model and FEA predictions with unloading (18 mph 

impacts)........................................................................................................................... 207

Figure 264. The effects of BC restraint on head impact response (25 mph coupler impacts). .. 208

Figure 265. Comparison of the 1D model and FEA predictions with unloading (25 mph coupler 

impacts)........................................................................................................................... 208

Figure 266. Comparison of the FEA and constant stiffness approximation. ............................. 209
xiii

Figure 267. Comparison of the 1D model and FEA predictions with unloading (fixed head 

stiffness - 18 and 25 mph impacts)................................................................................... 209

Figure 268. The effects of constraint BCs on the side impact response. ................................... 210

Figure 269. Comparison of models used to investigate reaction wall size effects. .................... 211

Figure 270. The effects of constraint wall width on the reaction loads. .................................... 212

Figure 271. The effects of wall width on the tank compression stiffness.................................. 212

Figure 272. The effects of wall width on the tank impact behavior. ......................................... 213

Figure 273. The effects of wall width on the impact force histories. ........................................ 214

Figure 274. The effects of constraint wall height on the reaction loads. ................................... 214

Figure 275. Comparison of Tank Deformations with different wall heights. ............................ 215

Figure 276. The effects of tank thickness on quasistatic compression loads. ............................ 215

Figure 277. The effects of tank thickness on quasistatic compression stiffness. ....................... 216

Figure 278. The effects of tank radius on quasistatic compression loads. ................................. 216

Figure 279. The effects of tank pressure on quasistatic compression loads............................... 217

Figure 280. The effects of tank pressure on quasistatic compression stiffness.......................... 217

Figure 281. Idealized schematic of the side impact spring mass model. ................................... 218

Figure 282. Idealized elastic-plastic spring behavior and calculated unloading response.......... 219

Figure 283. Comparison of the FEA and impact algorithm for different speed impacts............ 220

Figure 284. Comparison of the FEA and impact algorithm for different BCs........................... 221

Figure 285. Idealized schematic of the offset side impact model kinematics. ........................... 222

Figure 286. Comparison of the FEA and impact algorithm for offset side impacts................... 222

Figure 287. Comparison of the FEA and impact algorithm for an EO tank car......................... 223

Figure 288. Initial set of tank puncture forces under various impact conditions. ...................... 224

Figure 289. Effects of tank thickness on puncture force for various size impactors.................. 224

Figure 290. Tank thickness correction for the characteristic puncture force. ............................ 225

Figure 291. Effects of impact face orientation on puncture force. ............................................ 226

Figure 292. Effects of impactor shape on puncture force in 45-degree oblique impacts............ 227

Figure 293. Effects of impactor shape on puncture force in 30-degree oblique impacts............ 227

Figure 294. Effects of impactor shape on puncture force in 15-degree oblique impacts............ 228

Figure 295. Impactor shape corrected puncture forces for 45-degree oblique impacts.............. 228

Figure 296. Impactor shape corrected puncture forces for various oblique impacts. ................. 229

Figure 297. Impactor size correction for oblique impact puncture forces. ................................ 230

Figure 298. Correlation of characteristic puncture forces for various impact conditions........... 230
xiv 

Figure 299. Configuration of the layered punched plate protection concept (Yen, Kaste, 

Montgomery, Cheeseman, & Scott, 2011). ...................................................................... 232

Figure 300. Simulated tensile test behavior for the High Hard Steel. ....................................... 233

Figure 301. Simulated tensile behavior of the punched plate material...................................... 233

Figure 302. Comparison of the solid and punched plate tensile behavior. ................................ 234

Figure 303. Model for the punched plate concept impact analyses........................................... 235

Figure 304. Details of the model for the punched plate impact patch. ...................................... 235

Figure 305. Impact and puncture of the 500 lb chlorine car and punched plate protection........ 236

Figure 306. Calculated tank impact damage and puncture initiation......................................... 237

Figure 307. Calculated punched plate impact damage and puncture behavior. ......................... 237

Figure 308. Comparison of side impact puncture forces for different tank designs................... 239

Figure 309. Comparison of side impact puncture energies for different tank designs. .............. 239

Figure 310. Comparison of side impact puncture energies for different tank designs. .............. 240
xv 

Tables

Table 1. Tabular TC128B stress-strain curve values.................................................................. 28

Table 2. Summary of the baseline side impact analyses for the 105J600 tank car....................... 63

Table 3. Summary of the analyses to assess the impactor face edge radius................................. 65

Table 4. Summary of the analyses to assess the impactor orientation effects.............................. 79

Table 5. Summary of the baseline head impact analyses. ........................................................... 83

Table 6. Summary of the vertical offset side impact analyses. ................................................. 135

Table 7. Summary of the baseline side impact analyses on the 105J500 tank car ..................... 142

Table 8. Summary of the vertical offset side impact analyses on the 105J500 tank car............. 142

Table 9. Summary of the 45-degree oblique side impact analyses on the 105J500 tank car...... 143

Table 11. Summary of the ethylene oxide tank car design parameters...................................... 149

Table 13. Summary of the anhydrous ammonia tank car design parameters............................. 157

Table 15. Summary of the general-purpose tank car design parameters. .................................. 165

Table 16. Summary of impact analyses to assess outage volume effects. ................................. 169

Table 21. Parameter values for the spring-mass side impact algorithm .................................... 220

Table 22. Summary of side impact analyses for the 105J500 tank and punched plate concept . 238
xvi 

Revision Control Table

Revision Date Section Comments 

0 March 

2015 All Report No. DOT/FRA/ORD-13/17 - Original Technical 

Report 

1 Sept. 2023 Misc. Primary change to include assessment of the DOT-113 LNG 

tank car. Additional edits to update report from 2015 to 2023.

1 Sept. 2023 Acknowledgements Additional acknowledgements were added for the new 

research.

1 Sept. 2023 Introduction 

The need for assessing DOT-113 LNG tank car was added.

Additional relevant research performed since the original 

report was added to the background section.

1 Sept. 2023 2.2 Sections 2.2 and 2.2.1 were combined into Section 2.2.

1 Sept. 2023 5.7 A new section of the report was generated covering the 

puncture resistance assessment of the DOT-113 LNG tank car.

1 Sept. 2023 5.2.2, 5.3.5, 5.4.4 Additional information provided on head impact analyses for 

various tank head designs.

1 Sept. 2023 Conclusions Discussion on conclusions from new content added. 

Sept. 2023 References Multiple new references updated or added to the report.
xvii 

Acknowledgements

This report primarily describes analyses performed under the Federal Railroad Administration 

(FRA) Contract DTFR53-11-C-00017. The analysis methodologies used in this report build on 

the work previously performed under Next Generation Rail Tank Car (NGRTC) Project funded 

by The Dow Chemical Company. The development of the puncture modeling methodologies and 

the testing used to validate the models and develop the constitutive and failure models were 

performed under the NGRTC project. 

The analyses of Ethylene oxide tank cars in this report were performed under Contract No. 5058 

with the American Chemistry Council on behalf of its Ethylene Oxide Panel. The analyses use 

identical methodologies to those for the other tank car designs included in this study. 

Finally, the assessment of the cryogenic DOT-113C120W9 tank car for LNG service was added 

to Revision 1 of the report in 2023. The evaluation of the DOT-113 tank car was performed 

under Contract No. 693JJ622C000002 with the FRA. The support and collaboration of Francisco 

Gonzalez, III and Jeffrey Gordon of the FRA and Michael Carolan of the Volpe National 

Transportation Systems Center on this phase of the research was greatly appreciated. 
1 

Executive Summary

This report describes a research program to improve the safety and security of railroad tank cars. 

The approach used in the research and development program was to apply a tank impact and 

puncture prediction capability using detailed finite element analyses (FEA). The FEA capability 

was developed and validated previously in the NGRTC program. The analysis methodologies 

apply advanced damage and failure models that were developed using a series of material tests 

under various loading conditions and validated by full-scale tank car impact and puncture tests. 

In this study, the analyses were applied to investigate the tank puncture behaviors for a wide 

range of impact conditions. 

Different Size and Shape Impactors

In the initial phase of this program, different size and shape impactors were investigated. The 

impactors used included square, rectangular, and round impact face geometries. A new 

parameter was developed to characterize the effective size of the impactor. This impactor 

characteristic size is the square root of the area of the impactor face. The summary of the 

puncture forces for the various impactors is plotted against the impactor characteristic size in 

Figure 1. The figure shows that the impactor characteristic size parameter provides a good 

correlation for all the different impactor sizes and shapes analyzed. Overall, there is a strong 

linear correlation of the puncture force with the characteristic size of the impactor. 

Figure 1. Correlation of side impact puncture forces with ram characteristic size.

A similar summary of the puncture energies for the various impactors is shown in Figure 2. The 

figure shows that the impactor characteristic size parameter also correlates well to the impact 

energy for the range of impactors considered. There is more scatter in the correlation of the 

impact energies but that is expected since various factors such as the impact speed and boundary 

conditions (BCs) have been shown to introduce variations in the impact energy for different 

impact scenarios. The comparison of impact energies in Figure 2 show that the correlation is 
2 

roughly with the square of the characteristic size of the impactor. This is a result of the linear 

increase in the puncture force combined with a similar increase in the displacements required to 

reach the impact force (the puncture energy is obtained by integrating the force-deflection curve 

of the impact up to the point of the tank puncture). 

Figure 2. Correlation of side impact puncture energies with ram characteristic size.

The linear correlation between the puncture force and the impactor characteristic size is useful 

for defining the effective size of complex impactors. For example, the rail section impactor has a 

cross-sectional profile that includes both convex and concave regions. The puncture force for the 

rail has corresponds to a characteristic size of approximately 5 inches in a normal side impact. 

This falls within the expected range of values estimated from the rail profile. Alternatively, a 

more complex impactor, such as a coupler head can be assessed. Here the behavior is 

complicated by an impactor face profile that is not flat. As a result, the puncture force was found 

to vary significantly with relatively small changes in the orientation of the impact. For a limited 

set of impact orientations analyzed, the coupler head was found to have a characteristic size as 

small as 5 inches and as large as 12 inches. 

Impact Orientation Effects

To investigate the effects of the impactor orientation, as series of analyses was performed with a 

12x12 inch square impactor with a 0.1-inch edge radius. A summary of the analyses is provided 

in Figure 3 where the calculated puncture forces are plotted against the impactor rotation angles. 

The effects for the pitch rotation are similar to those for the yaw rotation, but with a slight 

variation in the puncture forces resulting from the relative stiffness of the tank for bending in the 

longitudinal and radial directions in the impact zone. The analyses where the yaw rotation was 

maintained at 45 degrees and various levels of pitch rotation were added further concentrates the 

load and damage at the corner of the impactor. 
3 

Figure 3. Puncture forces for the 12x12 inch impactor at various orientations.

For comparison, the puncture forces calculated for the rotated 12x12 inch impactor were used to 

calculate the impactor characteristic size, shown on the right axis of Figure 3. The plot shows 

that the characteristic size of the impactor decreases rapidly as the rotation increases from 0 to 

approximately 30 degrees. Between 30 and 45 degrees the contact is primarily with the edge or 

corner of the impactor and the puncture force (or characteristic size) is relatively constant. The 

characteristic size of the 12x12 impactor drops from 12 inches in the normal impact to 

approximately 4.5 to 5 inches in an edge impact. The characteristic size is further reduced to 

approximately 3 inches for the corner impact. These results show that impacting objects with 

corners and edges can have the penetration potential of a much smaller object if the orientation 

of the impactor concentrates the loading to the edge or corner. 

An impact condition with similarities to the rotated impactor is where the impact occurs at an 

oblique angle to the tank. A set of analyses was performed with the full range of impactor sizes 

and shapes at 15, 30, and 45-degree oblique impact angles. Comparisons of the normal and 

oblique impact puncture forces and energies are provided in Figure 4 and Figure 5, respectively. 

The puncture forces are reduced with increasing obliquity angles and at the 45-degree impacts 

the puncture forces are more than 50 percent lower for the largest impactors. However, as the 

impactor size is reduced the differences in puncture force are also reduced. At a 6-inch 

characteristic size the oblique impact puncture force is only reduced by 40 percent compared the 

normal impact. Finally, for the 3x3 inch impactor there is significantly less difference between 

the normal and oblique impact puncture forces. 
4 

Figure 4. Comparison of puncture forces for normal and oblique impacts.

Figure 5. Comparison of puncture energies for normal and oblique impacts.

The puncture energies for the oblique impact show similar trends to the puncture forces. The 

puncture energies for the largest impactors are reduced by roughly 60 percent. Again, as the 

impactor size is reduced, the differences in puncture energies are also reduced. At a 6-inch 

characteristic size, the oblique impact puncture energy is only reduced by 50 percent compared 

the normal impact. Finally, for the 3x3 inch impactor, there is very little difference between the 

normal and oblique impact puncture energies. 
5 

Head Impacts

A summary of the calculated head impact puncture forces and puncture energies for various size 

and shape impactors are compared to the side impact forces and energies in Figure 6 and Figure 

7, respectively. The slope of the puncture force fit is approximately 10 percent greater than that 

of the side impact puncture forces. The difference is a combination of two competing factors. 

First the combined head and head shield thickness is almost 50 percent thicker than the 

combined thickness of the tank shell and jacket. However, this increase in thickness is partially 

negated by the fact that the offset head impact scenario produces larger stress and strain 

concentrations at the top edge of the impactor that reduces the puncture force. 

Figure 6. Comparison of the calculated head and side impact puncture forces.

Figure 7. Comparison of the calculated head and side impact puncture energies.
6 

The comparison of the side and head puncture energies in Figure 7 show that again the head 

impacts have a similar fit to the square of the ram characteristic size, but the puncture energies 

are 30 percent to 35 percent lower for the head than for the shell. The difference primarily results 

from the head deformation mode and rigidly constrained impact scenario that are much stiffer 

than for the shell side impacts. As a result, the puncture forces are reached at significantly lower 

ram displacements resulting in the reduction of puncture energies. 

Side Impact Boundary Condition Effects

A series of analyses were performed to investigate the effects of the constraint level on the tank 

side impact response. The analyses were for the side impact of the 600 lb chlorine tank car. The 

impactor selected for these analyses was the 9.55-inch-diameter round impactor. Three different 

levels of constraint were considered: (1) highly constrained (2) moderately constrained and (3) 

unconstrained. The highly constrained boundary condition is the tank backed by the rigid impact 

wall that has been used for the majority of the side impact analyses in this report, as well as the 

previous NGRTC analyses (Kirkpatrick, 2009a). The unconstrained boundary condition is a 

single tank that is free to translate. The moderately constrained boundary condition is two 

deformable tanks sitting side-by-side. 

The impactor was prescribed to have a 15-mph constant velocity during the entire impact 

duration. This is more representative of the loading for an impactor that is attached to a longer 

section of train in a derailment where the very large mass results in small changes in impactor 

velocity over the duration of any individual impact event. A comparison of the force-deflection 

characteristics for the side impact response with the three different constraint conditions (wall, 

tank, free) is shown in Figure 8. For reference, a corresponding force-deflection curve for a 25-

mph impact with the 295,000 lb impactor is also shown on the graph. 

Figure 8. The effects of constraint conditions for the 15 mph constant velocity impacts.

The comparison shows that the initial portion of the force-deflection curves for all three 15 mph 

impacts are identical (up to approximately 30 inches ram displacement). All three impacts reach 
7 

an initial peak force that was very close to the failure level before the dynamic response of the 

tank results in a temporary drop in the impact force (at approximately 40 inches displacement). 

Beyond this time, the tank constraint BCs begin to play a large role in the behavior. With the 

highly constrained (wall) impact scenario the impact force quickly recovers, and the tank is 

punctured at approximately 48 inches of ram displacement. With the moderately constrained 

side-by-side tank scenario the impact force more slowly recovers, and the tank is punctured at 

approximately 56 inches of ram displacement. Finally, with the unrestrained (free) tank the 

impact force never fully recovers to the puncture force level and the tank does not puncture. 

The comparison of the different tank boundary constraints shows that the effects on the late time 

behavior and puncture energy can be significant. However, the initial portion of the loading is 

dominated by the inertial resistance of the tank and the puncture will occur in this initial phase of 

the impact for many combinations of impactor sizes and impact speeds. Thus, for many side 

impacts, the constraint on the back side of the tank is not significant. 

Head Impact Boundary Condition Effects

A series of analyses were performed to investigate the effects of the constraint level on the tank 

head impact response. The analyses were for the side impact of the 600 lb chlorine tank head 

with a 0.5-inch-thick head shield. The impactor selected for these analyses was the 9.55-inchdiameter round impactor. 

The baseline head impact conditions, adapted from the NGRTC program (Kirkpatrick, 2009a), 

were for a highly constrained tank head mounted on a test frame that does not allow for any 

motion at the specimen support. The head impact specimen included the tank head and head 

shield, supported by a short length of the tank shell and jacket, which were welded to a rigid test 

frame. To investigate the constraint effects in head impacts an unconstrained tank model was 

developed. The model includes the entire tank which is free to translate. Gravity was included in 

the analyses to develop appropriate vertical forces and motions in the offset impact scenario. 

Without the test frame support, a model of the ground was needed to resist the gravitational freefall motions of the tank. The tank is free to slide along the ground as a result of the impact. 

In the analysis of the unconstrained tank, the mesh-free Smoothed Particle Hydrodynamics 

(SPH) approach is used to model the lading. This has the advantage of being able to capture the 

fluid sloshing without mesh distortion effects and possible numerical instability of classical 

Lagrangian analyses. The SPH methodology is also compatible with the traditional Lagrangian 

analysis methodologies being used to evaluate the tank response. As a result, it is more 

computationally efficient than the Arbitrary Lagrangian Eulerian (ALE) methodology. 

The comparison of the force-displacement behaviors for 18 mph impacts with the 9.55-inchdiameter round impactor on the constrained and unconstrained tank heads is shown in Figure 9. 

For the constrained tank head, the force increases approximately linearly with displacement up to 

approximately a 1.8 million lb force at a displacement of approximately 25 inches. At this point 

the constrained tank head is punctured. However, the behavior for the head impact on the 

unconstrained tank is significantly different. The force-displacement curves for the 

unconstrained tank model start along the same force deflection curve. However, the force levels 

begin to drop below those of the constrained tank head at early displacement levels. This is 

because the impact forces push the tank away from the impactor reducing the rate of the 
8 

impactor head intrusion (dent formation). The impact forces level off and begin to drop at a force 

of approximately 1 million lbs and a displacement of 20 inches. The impact severity is well 

below the level needed to puncture the tank head for the unconstrained tank condition. 

Figure 9. The effects of tank motion BCs on head impact response.

The effect of the tank constraints for head impacts is observed much earlier in the response than 

for side impacts for two reasons. The first is that the tank cylinder is much stiffer in axial loading 

compared to lateral loading. Thus, the head impact forces are very rapidly transmitted to 

translations of the tank center of gravity (CG). The second reason for increased constraint effects 

in head impacts is the behavior of the lading. During the duration of the impact, only a fraction 

of the total lading mass is coupled to the motions of the unconstrained tank. This effect is shown 

by fringes of longitudinal velocity in the lading in Figure 10. The time shown is well past peak 

load, halfway through unloading. However, the bulk of the lading is still stationary (blue fringes 

in the figure). Only the regions of the fluid very near to the tank wall or directly behind the 

impacted tank head are moving. 

To investigate the effective weight of the fluid lading contributing to the motion in the head 

impact, we ran analyses at different smeared lading tank weights and iterated on an approximate 

equivalent weight of the tank. The value that matched the analysis best was a tank weight of 130

percent of the empty weight. The comparison of the analysis with the 130 percent tank weight 

with the empty tank model, the full weight model (smeared mass) and the model with SPH 

lading is shown in Figure 11. The agreement of the SPH model with the 130 percent tank weight 

model is quite good. Note that the 130 percent weight model increases the tank from an empty 

weight of 61,300 lbs to a weight of 79,690 lbs. The full weight of the tank is 263,000 lbs which 

is the empty tank plus approximately 200,000 lbs for the lading. As a result, these analyses show 

that less than 10 percent of the lading is coupled to the motion of the tank for this head impact 

scenario. 
9 

(a) Full tank profile (time=0.18 s)

(b) Impact zone (time=0.18 s)

Figure 10. Calculated longitudinal velocity distribution in the SPH lading.

Figure 11. The effects of lading on unconstrained head impact response.

Analysis of Other Tank Conditions and Car Designs

A set of analyses was performed to assess the effects of the tank and lading temperature. As the 

equilibrium temperature of the tank rises, the vapor pressure increases, and the liquid density is 

reduced. A decrease in the liquid density will produce an increase in the liquid volume with a 

corresponding reduction in the outage volume. Both increasing the pressure and reducing the 

outage can reduce the puncture resistance of a tank car. 
10 

The condition analyzed is a 105J600W chlorine tank car at an equilibrium temperature of 105o F. 

This temperature increases the internal vapor pressure for the tank to 155 psi and lowers the 

corresponding outage volume for a tank loaded to the specified limit to 7.5 percent. These are 

compared to the 100-psi internal pressure and outage volume of 10.6 percent at a tank 

temperature of 78 degrees F. 

A summary of results for both normal and oblique side impacts for the tank at higher temperature 

is given in Figure 12. In the figure, the calculated puncture energies at 105o F are normalized by 

the puncture energies at 78o F for the corresponding impact conditions. On average, the increase 

in temperature dropped the puncture energies by 20 percent. However, the puncture energies for 

smaller impactor sizes are more similar at the two temperatures. This is because the impact 

response for small impactors is dominated more by the structural stiffness. The internal pressure 

(and pressure increase) plays a smaller roll for the small dent sizes prior to puncture with the 

small impactor sizes. 

Figure 12. Normalized side impact puncture energies at 105o F.

In addition to the analyses performed on the 105J600 tank car, a series of other tank car types 

were analyzed. Evaluations were performed for the 500 lb chlorine tank car, the 340 and 500 lb 

anhydrous ammonia (AA) tank cars, the 300, 400, 500 lb ethylene oxide (EO) tank cars, and the 

DOT-113 LNG tank car. A full set of normal and 45-degree oblique side impacts were 

performed for each of the chlorine, EO, AA, and LNG tank car designs considered. For 

comparison of the various designs, the team normalized the calculated puncture energies all the 

various designs to those of the 105J500W chlorine tank car. The comparison for these 

normalized results is provided in Figure 13. 

In the comparison, the DOT-113 LNG tank car had the highest average puncture energy, which

was 126 percent higher than the 105J500W chlorine tank car. The average puncture energies for 

the 105J500W EO tank car design was the next highest and had the best puncture resistance for 

any of the pressure tank cars carrying Toxic Inhalation Hazard (TIH) materials. The EO tanks 
11 

had relatively high puncture energies because of the lower tank pressures and larger diameter 

tanks. The 105J500W, 105J400W, and 105J300W EO tank cars had puncture energies on 

average 82 percent higher, 17 percent higher, and 12 percent lower, respectively, than the 

105J500W chlorine tank car. The puncture energies for the 105J600W chlorine tank car were on 

average 37 percent higher than the 105J500W chlorine tank car. The 112J500W and 112J340W 

AA tank cars were on average 10 percent above and 39 percent below the 105J500W chlorine 

tank car, respectively. 

A similar comparison of the relative head impact puncture energies is shown in Figure 14. 

Again, the DOT-113 LNG tank head had the highest puncture resistance with an average 

puncture energy 56 percent higher than the 105J500W chlorine tank head. 

Figure 13. Comparison of relative tank shell puncture performance for different designs.

Figure 14. Comparison of relative tank head puncture performance for different designs. 
12 

Analytical Models of Tank Car Impacts

The FE modeling approach is very useful for determining the mechanics of tank impacts and 

punctures. However, at times, a simplified analysis methodology or impact algorithm is useful 

for the assessment of various factors on tank impact safety. In this study, we developed 

analytical tank impact algorithms that can be applied for future analyses of tank car safety. When 

evaluating appropriate analysis methodologies, we examined the response characteristics of both 

head and side impacts. We found that the behaviors for these two impact conditions are 

sufficiently unique that different analysis methodologies were appropriate. 

The head impact response has several characteristics that influenced the simplified impact 

algorithm. The tank head is a stiffer structure under impact and the impact behavior for a 

constrained head is relatively independent of the impact speed. The most common head impact 

scenario is with the motions and orientations of the impacted and impacting cars nearly aligned 

with the original direction of travel. As a result, the motions can be assumed to be primarily one 

dimensional. In addition, the contributions of the lading response are significantly different for 

head impacts on unconstrained tanks. 

A simple 1D algorithm was developed for the head impact tank motions with the different 

constraint conditions. The algorithm uses a known force-deflection curve of the fully constrained 

tank head as a characteristic property of the tank structure. The forces are then used to update the 

tank and impactor motions. The relative displacement of the impactor and tank are used to 

calculate an updated tank depth and corresponding change in impact force. 

The force-deflection behaviors predicted by the simple 1D algorithm for the two unconstrained 

tank impacts with the empty and full tank weights are compared to the detailed FE analyses in 

Figure 15. The comparison shows that the simple algorithm accurately reproduces the force 

versus dent depth interaction and tank motions for the full impact and unloading behavior. 

Figure 15. Comparison of the 1D model and FEA of head impact behaviors.
13 

The side impact response also has several characteristics that influenced the methodology 

applied for the simplified impact algorithm. The tank is a more compliant structure under side 

impacts and the impact behavior is not independent of the impact speed (dynamic effects – see 

Section 3.4). The side impact scenarios typically occur as a result of large-scale lateral buckling 

behaviors in a derailment where the motions of the various cars are chaotic. As a result, the side 

impacts will include a greater range of variability in impact location and orientation and the 

motions will be at least two dimensional. These characteristics required a unique analytical 

methodology for side impacts. 

The approach used to develop a side impact analysis algorithm is to develop a spring-mass 

model for the tank that can replicate the force-deflection characteristics for side loading against 

various objects (e.g., impactor, reaction wall). These loads can then be applied with equations for 

the tank kinematics under the combined actions of the loads. A schematic of the spring-mass 

system used for the side impact algorithm is shown in Figure 16. The tank is represented by a 

series of five symmetric masses connected by springs. The outer masses (M1) are small and 

represent a small region of the tank that is involved with the initial interaction with the impactor 

or reaction structures. The secondary masses (M2) represent the region of the tank in the 

deformation zone around the impactor or reaction structures that become significant as the 

deformation progresses. The central mass (M3) is the remainder of the tank mass. 

Figure 16. Idealized schematic of the side impact spring mass model.

The values used for the spring-mass model parameters were derived in a two-step fitting process. 

Initially, a series of Monte-Carlo analyses were performed where the parameters were allowed to 

vary randomly, within ranges determined by physical constraints. Results were compared to a 

series of FE impact analyses and the correlation for each set of parameters was determined. 

Subsequently, the parameters that provided the best fit to the impact data were optimized by 

finding the minimum error in the parameter space around the initial Monte Carlo parameter set. 

The resulting model was then applied to simulate a series of impact behaviors and the results 

were compared to the corresponding FE analyses. For example, a series of impacts with the 9.55-

in-diameter impactor at different impact speeds are compared in Figure 17. The comparison 

shows that the spring-mass model does a good job of reproducing the variations in impact 
14 

behaviors produced by different speed impacts. Note that the spring-mass model does not include 

puncture prediction, so the comparison of the higher speed impacts is only appropriate up to the 

point of the calculated tank punctures in the FEA. 

Figure 17. Comparison of the FEA and impact algorithm for different speed impacts.

Development of the Characteristic Puncture Force

The above sections describe analyses that can predict the force-deflection behaviors. However, 

the point along the force-deflection curve at which the tank is punctured also needs to be 

determined. This puncture force will be dependent on both tank geometry (materials and 

thicknesses) and the impact conditions (impactor size and impact orientation). 

Our approach to developing a tank puncture criterion for the tank impact algorithm(s) was to use 

puncture data from all the detailed FE puncture analyses described in this report and develop a 

“characteristic puncture force” parameter that is a function of the impactor characteristic size. A 

collection of the calculated puncture forces for various tank and impact conditions is shown in 

Figure 18. As expected, there is a general trend in the data with increasing puncture loads for 

increasing ram characteristic size. However, for any given ram characteristic size, there is a large 

spread in puncture forces. This is because the puncture force for an oblique impact against a 

111A100W1 tank car will be much lower than the puncture force for a normal impact against a 

105J600 tank car. 

To develop a characteristic puncture force, we applied a series of correction factors for the tank 

thickness, impact orientation, and impactor shape. When we apply all the corrections, we obtain 

the characteristic puncture force correlation as shown in Figure 19. Using this characteristic 

puncture force allows us to assess the puncture conditions for a wide range of tank and impact 

parameters. The uncertainties in the puncture force can be assessed by comparing the range of 

errors in the corrected data for the detailed FE analyses to the puncture data fitting line. 
15 

Figure 18. Initial set of tank puncture forces under various impact conditions.

Figure 19. Correlation of characteristic puncture forces for various impact conditions.

Analysis of Real-World Threats

The majority of this study was focused on the safety of tank cars in accidents and derailments. 

These events that occur as part of normal rail operations are the most common events that lead to 

releases of hazardous materials in rail operations. However, the security of tank car from an 

intentional attack is also a consideration for these designs. The Department of Homeland 

Security (DHS) has done several small- and full-scale tests of components and tank cars 

subjected to different acts of terrorism. The objective of the analyses performed in this effort was 
16 

to assess the puncture performance in impacts (safety) of a protection concept developed by DHS 

for security against various threats. 

The protection system concept analyzed was the punched plate concept. The system consists of 

two 1⁄4-inch-thick perforated panels made of High Hard Steel (HHS). The perforations were 3/8-

inch diameter holes in a hexagonal pattern with 1⁄2-inch spacing between the nearest neighbor 

hole positions. The two panels are used in an offset configuration. 

A series of tank side impact puncture analyses was performed on the punched plate protection 

concept. The analyses showed that the protection concept also performs reasonably well in 

impact conditions. A comparison to other jacket designs found that the punched plate system 

provided equal or better impact protection than an equivalent weight TC128B jacket. Thus, this 

concept looks like a good design alternative that can provide protection for both safety and 

security concerns. 
17 

1. Introduction

There is ongoing research to develop strategies for improving railroad tank cars so they can 

maintain tank integrity for more severe accident conditions than current equipment. Research 

results are being used to develop improved tank car designs and to inform rulemaking by the 

Federal Railroad Administration (FRA). 

A significant portion of the tank car research was performed under the Next Generation Railroad 

Tank Car (NGRTC) Program (Kirkpatrick, 2009a). A key effort in the NGRTC Program was the 

development and validation of detailed finite element (FE) models of tank car equipment which 

can accurately predict the puncture resistance under different impact conditions. To date, these 

analysis tools have been developed and validated for the puncture of the baseline tank cars for 

both side and head impact conditions. These validated tools are being applied in this study to 

assess the puncture resistance of various tank car designs under various impact conditions. 

This report describes the application of the validated puncture analysis capabilities to assess the 

effects of different impactor threats and impact conditions. The scope of this effort includes the 

development of detailed FE models for tank cars and impactors, and the use of those models for 

various impact scenarios to assess puncture conditions. 

1.1 Background

Accident statistics show that the rail industry’s safety performance has generally improved over 

the last few decades. The FRA’s Railroad Accident and Incident Reporting System (RAIRS) 

show that the number of accidents per year with at least one car releasing hazardous materials 

has decreased significantly over the past 25 years, as shown in Figure 20 (FRA, 2023). However, 

a series of three recent accidents or derailments involving the release of hazardous material have 

focused attention on the structural integrity of railroad tank cars. These events include (1) Minot, 

ND, on January 18, 2002 (NTSB, 2004); (2) Macdona, TX, on June 28, 2004 (NTSB, 2006); and 

(3) Graniteville, SC, on January 6, 2005 (NTSB, 2005). 

Following these incidents, a series of research programs were initiated to develop strategies for 

improving railroad tank cars to maintain their structural integrity for more severe accident 

conditions. A significant portion of this research was performed under the Next Generation 

Railroad Tank Car (NGRTC) Program (Kirkpatrick, 2009a) (2009b) (2009c) that was performed 

from 2006 through 2010. The NGRTC program was initiated by The Dow Chemical Company, 

Union Pacific Railroad, and Union Tank Car Company, working with the FRA and Transport 

Canada (TC). The NGRTC program included full-scale tank car impact testing, material and 

component testing, development and application of tank car impact and puncture modeling, and 

efforts to design and evaluate advanced tank car impact protection concepts. A key outcome of

the NGRTC Program was the development and validation of detailed FE models of tank car 

equipment that can accurately predict the puncture resistance under specified impact conditions. 

These tank car impact and puncture modeling capabilities have supported all the subsequent tank 

car safety research efforts. 
18 

Figure 20. Number of Rail Accidents Releasing Hazardous Materials (FRA, 2023). 

In collaboration with the NGRTC efforts, FRA initiated a significant research program to 

improve tank car safety, which is still ongoing. An important contribution of this FRA research 

has been a series of full-scale impact tests on tank cars and the related analyses of the impact test 

conditions. A summary of the full-scale tank car impact tests and associated analyses (2007-

2019) is provided by Krishnamurthy et al. (2022). 

One limitation of the effort in the NGRTC program is a primary focus on a few idealized impact 

conditions such as a normal impact (an impact that is perpendicular to the tank surface) with a 6-

inch by 6-inch square impactor. Similarly, most of the subsequent full-scale tests performed by 

FRA were conducted using a 12-inch by 12-inch square impactor (Krishnamurthy, et al., 2022). 

However, there is uncertainty as to how representative these idealized impact conditions are as 

surrogates for the real-world critical impact threat environment. 

In a parallel research effort, the Railway Supply Institute (RSI) and Association of American 

Railroads (AAR) have an ongoing project to evaluate the safety of tank cars. The RSI-AAR 

Railroad Tank Car Safety Research and Test Project used an alternate approach of collecting and 

analyzing extensive information about tank car performance in train accidents [e.g., (Barkan, 

Ukkusuri, & Waller, 2005), (Saat & Barkan, 2005)]. In over 50 years, the effort has collected 

data on more than 50,000 damaged tank cars and 31,000 accidents (Saat & Barkan, 2005). 

Analysis of these accident data allows for the assessment of the Conditional Probability of 

Release (CPR) of a tank car carrying hazmat in a train accident for a given tank car design. The 

CPR is available for the existing tank car types in the database, allowing for an assessment of the 

change of CPR when the hazmat shipment is moved by a tank car with different design features. 

However, this approach cannot provide information on CPR for a novel tank car design that 

varies from existing practices. 

The initial set of research projects above had addressed two fundamental and separate aspects of 

tank car safety, as illustrated in Figure 21. The research performed by NGRTC and FRA 

included deterministic analyses and testing of tank cars under ideal conditions. This included 
19 

both traditional tank car designs as well as novel tank car concepts proposed for enhanced impact 

protection. However, there was not a capability to quantitatively show how the increased 

puncture resistance obtained in these idealized impact conditions would result in reduced 

releases under service conditions.

Figure 21. A graphical illustration of the initial tank car safety research areas. 

In contrast, the RSI-AAR Railroad Tank Car Safety Research and Test Project was focused on 

the performance of existing tank car designs under the impact threat environments produced by 

real-world service conditions. However, since the program was based on the statistical

performance of tank cars in service, there was no way to predict how a novel tank car design 

would perform when introduced into the freight rail fleet. 

After the completion of the NGRTC program, additional research for tank car safety 

improvements was performed under the Advanced Tank Car Cooperative Research Program 

(ATCCRP), which was initiated to coordinate research efforts to enhance the safety and security 

of rail tank car shipments of Toxic Inhalation Hazard (TIH) materials. The ATCCRP was built 

on prior and ongoing research conducted by the NGRTC Project, the Chlorine Institute tank car 

safety research (Anderson & Kirkpatrick, 2006) (2007), and the RSI-AAR Tank Car Safety 

Research and Test Project (Railway Supply Institute, 2009), (Treichel, et al., 2019). The 

ATCCRP was a joint effort of shippers of tank cars, railroads that transport hazmat, and railroad 

tank car builders and lessors. In addition, Memoranda of Cooperation were developed to 

formalize cooperation agreements between ATCCRP participants and USDOT - FRA, TC, the 

U.S. Department of Homeland Security (DHS) - Transportation Security Administration, and the 

DHS Science and Technology Directorate.

The ATCCRP was organized by first collecting a wide range of topics for Technical White 

Papers (TWP) on potential technologies that could improve the safety and security of tank cars. 

These topics included the following (some numbers are missing because similar topics were 

combined): 

• TWP-1: Effect of Pressure on Puncture Resistance – Chlorine and Anhydrous 

Ammonia
20 

• TWP-3: Reducing Dispersion Effects by Lading Temperature Reduction

• TWP-4: Sandwich Tank Car Design 

• TWP-5: Composite Materials for Protection Systems

• TWP-6: Structural Foams and Adhesives

• TWP-9: Coupler Modifications

• TWP-10: Correlating Material Properties to Puncture Resistance

• TWP-11: Relating Conditional-Probability-of-Release to Modeling and Tests

• TWP-13: Other TIH Materials

• TWP-14: Analysis of Different Impactor Threats and Impact Conditions

• TWP-15: Development of Performance-Based Testing Requirements for Railroad Tank 

Cars

• TWP-16: Application Study for Perforated Armor Plating

• TWP-17: Revising and Updating Conditional Release Probability Estimates

• TWP-18: Forensic Analyses and Elimination of Real-World Failures

• TWP-19: Improvements in Tank Car Weld Safety

• TWP-20: Investigation of Impactors in Past Accidents

• TWP-21: Demonstrate Approval Protocols on Candidate Technologies

• TWP-22: Development of Advanced Head Protection Concepts

The ATCCRP participant organizations reviewed and ranked the merits of the TWPs including 

anticipated commercial feasibility, estimated costs, and proposed schedules. Each organization 

identified the five TWP projects they believed were most important and likely to provide 

meaningful results. A system was worked out and used to identify interdependencies between 

projects and rate the proposed TWP research against the following ATCCRP objectives: 

• Improved puncture resistance

• Reduce releases at top fittings

• Mitigate potential security threats

• Provide a basis for possible use in establishing regulatory standards and protocols for 

performance tests

• Enhance security, situational awareness, and tools for emergency responders

Following this evaluation and rating process, the ATCCRP Committee decided to perform 

projects TWP-4, 5, 10, 11, 14, 15, 17, and 22 (Kirkpatrick, 2018). 

Among these TWPs, two were selected to form a connection between the two thrust areas of tank 

car safety research, shown previously in Figure 21. The expansion in the areas of research 
21 

developed by these two projects is illustrated in Figure 22. The TWP-11 project was initiated 

with the objective to better define the collision threat under real-world service conditions

(Kirkpatrick, et al., 2023). To support this goal, the TWP-11 project developed and applied 

detailed FE methodologies to analyze the kinematics of freight trains in derailments and 

collisions [e.g., (Kirkpatrick, et al., 2023), (Kirkpatrick, et al., 2022)]. The models were then 

validated by quantitative comparisons to real world derailments. An example derailment 

simulation is shown in Figure 23 for the October 7, 2011, derailment in Tiskilwa, IL (NTSB, 

2013). Evaluation of the derailments and collisions has shown that these are complex events with 

a wide range of collisions between the various cars and equipment in the train. 

Figure 22. Summary of tank car safety research including ATCCRP Projects. 

Figure 23. Detailed FE simulation evaluation for the Tiskilwa, IL derailment. 

The second project was the TWP-14 project performed under FRA sponsorship. This project 

applied deterministic tank car impact analyses under a much wider range of impact conditions 

including various shape and size impactors, offset impact conditions, and oblique impacts. This 

project was carried out in 2013 and is the study documented in the initial revision of this report 

Direction 

of travel

Direction 

of travel
22 

(Kirkpatrick, 2013). With the TWP-14 methodology, the tank impact resistance was not limited 

to a single idealized impact condition but rather evaluated over a wide range of potential impact 

scenarios. 

After the completion of this initial TWP-14 research project in 2013 (Kirkpatrick, 2013), an FRA 

ruling was made that allows transport of LNG in DOT-113C120W9 tank cars. This will likely 

result in an increase in shipments of LNG by rail in the near future. FRA has an ongoing fullscale test program to address the puncture resistance of these tank cars. However, these tests are 

being performed under ideal impact conditions and to date have applied a relatively large 12-inch 

by 12-inch impactor. Since these are novel tank designs, there is a risk that under different 

impact conditions (e.g., smaller impactors) the puncture resistance displayed with these tests of 

the DOT-113C120W9 tank cars relative to other designs may not be proportional. It was 

important to identify if this type of vulnerability exists in the design before a significant fleet is 

put into service. As a result, the study is revised in this report to assess the puncture resistance of 

the DOT-113C120W9 under a variety of impactors and impact conditions and compare the 

relative puncture resistance to other designs. 

In addition to the assessment of the DOT-113C120W9 tank car, this report was also revised to 

include relevant ATCCRP impact results that were completed subsequent to the original TWP-14 

study [e.g., (Kirkpatrick & McKeighan, 2018), (Kirkpatrick, 2017)]. The results included are 

primarily additional head impact assessments of the various tank car designs.

1.2 Material Damage and Failure Behaviors

A necessary component of the predictive tank car puncture modeling capability applied in this 

study is a detailed model that can be used to determine the impact damage and failure of the tank 

and protective system materials. An extensive program of laboratory materials testing was 

performed in the NGRTC Program (Kirkpatrick, 2009a) to characterize the tank car materials of 

interest. The tests included various material characterization tests, such as notched tensile tests 

and combined tension/shear tests, used to calibrate the material constitutive and failure behavior. 

Strain rate effects on the tank car materials were investigated and found to not have a significant 

effect on the tank puncture behavior. Additional component tests, such as punch tests and bend 

tests, were performed to validate the constitutive models. 

The material damage and failure model applied is the Bao-Wierzbicki (BW) model that defines 

the material damage development based on the current stress state in the material and the plastic 

strain increments. The critical strain function is that proposed in the BW criterion and contains 

multiple branches depending on the range of stress state. For completeness, the NGRTC material 

testing and failure model development efforts are summarized in Section 2 of this report.

1.3 Tank Car Puncture Modeling

The BW failure modeling capability was combined with the tank car model to complete the tank 

car puncture prediction capability. This combined tank car impact and puncture modeling 

capability was applied in the NGRTC program (Kirkpatrick, 2009a) to evaluate a wide range of 

tank/jacket and head/head shield geometries. The side impact condition was a normal impact 

centered on the belt line of the tank. The head impact condition was an offset impact point 

approximately 29 inches vertically downward from the center of the head. 
23 

An example head impact and puncture analysis is shown in Figure 24. The head impact analyses 

included the head, head shield, and a sufficient length of the side shell and jacket to allow for 

buckling to initiate in the jacket support from the loads transmitted by the head shield, as seen in 

Figure 24. 

(a) Initial impact conditions (b) Puncture response of the head

Figure 24. Calculated puncture behavior of a head and head shield.

The calculated head and shell puncture forces as a function of the combined tank and jacket (or 

head shield) thickness is shown in Figure 25. All the analyses included in the figure are 

performed with the 6x6 inch impactor with a 1⁄2-inch edge radius (the standard impactor in the 

NGRTC program). The figure shows the analyses are mostly consistent with a linear relationship 

between puncture force and total thickness of the protective layers. 

Figure 25. Calculated puncture forces as a function of system thickness.
24 

The linear relationship between the puncture force and total tank system thickness provides an 

indication of the primary failure mechanism initiating the tank puncture. The geometry of the 

ram impacting and indenting a pressurized tank shell is shown in Figure 26(a). A force balance 

analysis in the direction of the impact on a patch of tank shell material is shown in Figure 26(b). 

The forces resisting the impact loads are the pressure on the inside surface of the contact patch 

and the shear stress around the perimeter of the contact patch. For a 100-psi tank pressure and a 

6x6 inch impactor, the resultant force from the pressure is less than 4 kips on the contact patch. 

Thus, the average shear stress is approximately equal to the impact force divided by the product 

of the impactor face perimeter and tank thickness. 

The slope of the linear fit in Figure 25 corresponds to an average shear stress in the tank layers 

around the perimeter of the impactor of 39 ksi. By comparison, the yield and ultimate stress 

levels of the TC128B in pure shear are 33 ksi and 49 ksi, respectively (approximately 58 percent

of the stress values in pure tension using a Von Mises yield criterion). Thus, the force balance 

indicates that the failure mode is primarily exceeding the shear capacity around the perimeter of 

the impact patch. 

The calculated puncture forces for pressurized heads and the thicker head systems tended to fall 

slightly below the linear fit in Figure 25. The proposed mechanism for these lower forces is that, 

for the stiffer head systems, the offset impact creates a larger stress concentration along the upper 

edge of the impactor face and the failure initiates at that location at a lower total force. The more 

compliant head systems allow for a larger dent to form, and the impactor develops a more 

uniform stress distribution in the impact patch around the ram face perimeter. 

(a) Geometry of the tank indentation

(b) Free body diagram for the tank contact patch

Figure 26. Loading and failure mechanism for the tank impact and puncture.
25 

2. Material Constitutive and Damage Models

2.1 Introduction

The tank car impact analyses require a model for the material constitutive and damage behaviors 

to accurately predict the puncture threshold under various impact conditions. A piecewise linear 

elastic-plastic constitutive model was modified for this purpose to include a version of the BaoWierzbicki (BW) failure criterion [ (Bao & Wierzbicki, 2004a), (2004b), (Lee & Wierzbicki, 

2004)]. This model has been applied by other researchers to assess tank car puncture conditions 

(Tang Y. , Yu, Gordon, Jeong, & Perlman, 2008) and is capable of reproducing both the 

nonlinear stress-strain behavior of the material as it deforms into the plastic regime and the 

fracture and failure behavior that depends on the state of stress and plastic strain history in the 

material. The material parameters used in these constitutive models were developed from the 

material test data on TC128B steel, developed under the NGRTC program [e.g., (McKeighan, 

2007a), (2007b) (2007c)]. 

The following sections describe the development of the constitutive and damage parameters used 

in the subsequent tank car puncture analyses. 

2.2 TC128B Material Properties 

The first step in the development of a constitutive model is the development of the nonlinear 

stress-strain behavior. This governs the mechanical response of the material and prescribes the 

internal forces (stress) that are developed as the material is deformed (strained). 

A tabular stress-strain curve was developed based on testing of different samples of TC128B 

(McKeighan, 2007a). A series of standard tensile tests were performed on different batches of 

TC128B, as shown in Figure 27. The data is consistent within each batch of material, but 

significant variation can be found in tank car material obtained from different sources. The new 

material that was tested was at the upper range of strength for TC128B and the material 

recovered from the tank cars used in the test were more consistent with previous test data [e.g., 

(NTSB, 2003)]. As a result, the material recovered from the tank car used as the Test 2 target 

vehicle was used as the baseline material for the analyses in this report. 

The data shown in Figure 27 is the measured engineering stress-strain behavior. Engineering 

stress was obtained by dividing the measured loads by the original cross-sectional area of the 

specimen. Similarly, engineering strain was obtained by dividing the change in the specimen 

gauge-section length by the original length. 

The constitutive model in the finite element analyses requires that the engineering data be 

converted to true stress and true strain. This conversion accounts for the changing cross section 

of the specimen as it was deformed. The specimen cross section changes (shrinks) significantly 

during the test, and the engineering stress does not yield the “true” stress in this cross section. 

Similarly, the engineering strain is not representative of the material behavior, especially when a 

general three-dimensional state of strain exists. As a result, the engineering stress decreases as 

some materials approach failure, implying a weakening of the material. In reality, the stress in 

the cross section is increasing due to the reduction in the cross-sectional area (i.e., necking).

27 

After the onset of localization, the determination of the true strain in the necked region becomes 

more complex and requires measurement of the local neck geometry.

The TC128B engineering test results are compared to the converted true stress and true strain 

data in Figure 28. The true stress curves from the tests do not include a correction for the necking 

behavior. As a result, they are only valid up to the onset of necking at a true strain of 

approximately 15 percent. The actual true stress and true strain curves for the material continue 

to strain harden throughout the loading if the effects of necking were corrected. An extrapolated 

true stress curve that corrects for the effects of the necking behavior is added to Figure 28 (solid 

black line). It is this extrapolated curve that is used in the material constitutive model. 

The final step in obtaining the tabular stress-strain parameters for the TC128B constitutive model 

was to fit a smooth set of points to the extrapolated true stress data. This final tabular fit for the 

TC128B is shown in the true stress versus plastic strain curve in Figure 29. The specific values 

for the tabular stress-strain curve are also listed in Table 1. As a validation that this curve 

accurately captures the true stress-strain behavior of the material, a tensile specimen model was 

generated, and the constitutive parameters were applied to simulate the tensile test response. The 

calculation was analyzed to determine the engineering stress-strain behavior consistent to the 

tests (e.g., using equivalent gauge section length). A plot of the calculated engineering behavior 

compared to the test data is shown in Figure 30. The data shows that the constitutive parameters 

accurately reproduce the material behaviors including the onset and development of necking in 

the specimen. 

Figure 28. Comparison of engineering and true stress-strain data for TC128B.
28 

Figure 29. Tabular true stress curve developed for the TC128B constitutive model.

Table 1. Tabular TC128B stress-strain curve values

Point No. Plastic Strain (in/in) True Stress (ksi)

1 0.00e+00 58.0

2 8.22e-04 54.6

3 1.30e-02 54.8

4 2.76e-02 66.5

5 5.41e-02 79.5

6 9.87e-02 90.2

7 1.49e-01 96.0

8 1.15e+00 165.0

Figure 30. Comparison of the measured and calculated TC128B tensile test.


31 

The parameters A and B in Equation 7 can be determined by a series of tests under different 

stress conditions including notched tensile tests with specimens of varying notch radii 

(Mackenzie, Hancock, & Brown, 1977) and tensile-shear tests with different ratios of tension to 

shear stress. 

Figure 32. Bao-Wierzbicki failure surface and tests used for model calibration.

2.4 Material Characterization Testing and Analyses

A wide variety of material characterization tests were performed to calibrate and validate the 

material constitutive and failure models. These include material tests such as standard tensile 

testing to assess the material stress-strain behavior and testing under various stress states 

(notched tensile or tensile-shear tests) to obtain the characteristics of the failure surface. 

Subsequent tests under more general loading conditions, such as the punch test configuration, are 

used to validate the models. The approach applied here is to perform detailed analyses of the 

material testing conditions to assess the accuracy and validity of the models. The comparisons 

for the different testing conditions are provided in the following sections of this report. 

2.4.1 Tensile Tests and Analyses

Standard tensile test methods were employed in accordance with ASTM E8 (McKeighan, 

2007a). The thick TC128B allowed fabrication of a round tensile specimen (diameter of 0.505-

inch). For all other materials a flat specimen, as shown in Figure 33, was utilized. The specimen 

had a gage length of 2-inch. No machining was performed in the thickness direction, and it was 

tested as received. 

Photographs of the TC128B round bar specimens that were tested are provided in Figure 34. An 

extensometer with a 2-inch gage length was mounted on the specimen during testing. In one 

case, the thickest TC128B condition, strain gages were also mounted (2 gages, oriented opposite 

of each other) on the specimen gage length. Due to the excellent agreement between the strain 

gage and extensometer results, strain gages were omitted in all subsequent testing.
32 

Figure 33. Dimensions of the specimen used in tensile testing.

Figure 34. Necking behavior observed in the TC128B round bar specimens.

All tests were performed in constant-rate displacement control. Two rates were used, either 0.035 

or 0.050 inch/minute. Due to the large elongation observed in the steel materials, typical test 

times ranged from 15-30 minutes under the constant displacement testing. The data acquisition 

system was configured to record data at 3 Hz.

To confirm that the tensile test data reduction and material constitutive parameter extraction 

process was performed correctly, a model of the tensile specimen was generated, and the tensile 

test was simulated using the constitutive model. The load and displacements were extracted from 

the analysis using consistent methodologies to the test. A comparison of the measured and 

calculated engineering stress-strain behaviors for TC128B is shown in Figure 35. The 

comparison shows that the model accurately reproduces the stress-strain behavior and captures 

the initialization of the necking response. 
33 

Figure 35. Validation of the tensile test behavior for TC128B.

2.4.2 Notched Round Bar Tensile Tests and Analyses

The notched round bar tensile tests were used to assess the performance of the BW failure model 

in the high stress triaxiality regime. The tests were performed using round bars with various 

notch radii (McKeighan, 2007b) to achieve different levels of confinement at the notch root and 

thus different stress triaxiality levels. Models were created for the different notched round bar 

specimens and the tests were simulated. 

Material was provided from the two full-scale tank shell test articles (Tests 1 and 2) in the form 

of 12x12-inch plates. These plates were taken from near the impact site and were fabricated from 

normalized TC128B with a thickness of 0.777-inch. Specimens were extracted from these plates 

for mechanical testing. All specimens were oriented in the transverse orientation relative to the 

original plate rolling direction. The transverse orientation of the plate used to fabricate a tank car 

ring segment corresponds to the axial direction of the tank.

The notched tensile testing was performed similar to the procedures of the conventional tensile 

test standard, ASTM E8. The inner net diameter of the notched specimen is 0.25-inch, and the 

gross outer diameter is 0.5-inch. The three different notch geometries, with radii of 0.25, 0.10 

and 0.05-inches, were all gripped in smooth clamping friction grips. A photograph of the test 

setup is shown in Figure 36. 

A comparison of the calculated and measured stress-strain behavior across the notch for the three 

different radii specimens is shown in Figure 37. The comparison shows that the constitutive and 

damage model were capable of reproducing both the increase in stress level and reduction in 

ductility that occur as the notch radius is reduced. The BW failure parameters used provide a 

good correlation to the observed failures of the specimens. 
34 

Figure 36. Test setup for the TC128B notched round bar specimens.

Figure 37. Validation of the notched round bar test behavior for TC128B.

2.4.3 Tensile-Shear Tests and Analyses

The combined tensile-shear tests were used to assess the performance of the BW failure model in 

the low stress triaxiality regime (stress triaxiality between 0 and 1/3). The tests were performed 

using a modified Arcan specimen (Arcan, Hashin, & Voloshin, 1978) to achieve different ratios 

of tensile and shear by rotating the orientation of the gauge section relative to the loading axis, as 
35 

shown in Figure 38. A photograph of the test setup is shown in Figure 39. Instrumentation 

includes clip gauges across both slots separating the upper and lower specimen sections, a string 

potentiometer to measure the displacement along the load path, the load ram LVDT, and the load 

cell. The tests were performed in a displacement control mode at a rate of 0.002 inch per second 

and data was collected at 5 Hz. 

Simulations of the specimen geometry were initially performed to assess that a relatively 

uniform stress state could be achieved in the specimen gauge section, as shown in Figure 40. 

Models were then created for each of the specimens with different gauge section orientations and 

the tests were simulated. A comparison of the calculated and measured load-displacement 

behaviors is shown in Figure 41. The comparison shows again that the constitutive and damage 

model could reproduce both the decrease in load level and increase in displacement that occur as 

the orientation was rotated from pure tension to pure shear. The BW failure parameters used 

provide a good correlation to the observed failures of the specimens. 

Figure 38. Specimen geometries for the combined tensile shear tests.

Figure 39. Photograph of the combined tensile shear test configuration.
36 

Figure 40. Analysis of the specimen behavior in the pure shear orientation.

Figure 41. Validation of the combined tensile shear test behavior for TC128B.

2.4.4 Punch Tests and Analyses

The above notched round bar and tensile shear tests provide a good set of data to validate that the 

BW failure model can predict the damage development and failure of the TC128B material for a 

wide range of stress states. However, these tests were used to assess only the failure parameters

A and B in Equation 7. Therefore, an independent punch test was developed and applied to 
37 

validate that the model could predict the failure of the material under a more general loading 

condition. 

The specialized puncture fixture was developed for the NGRTC program at the SwRI Materials 

Test Lab and installed in a 220-kip test machine as shown in Figure 42. The punch test fixtures 

are shown with the 1.5-inch diameter punch and the 3-inch diameter receiving hole bore (socalled manhole cover). The fixture was designed so that different punch sizes and different 

manhole cover diameters can be used. 

The punches were fabricated from hardened bar stock material. The punch contact face was flat 

with a 0.30-inch radius around the perimeter. Punches were fabricated with diameters of 1.0, 1.5, 

2.0 and 3.0 inches. Manhole covers were fabricated with hole diameters of 2.0, 2.5, 3.0, 3.5, 4.5, 

and 5.5 inches. As a result, the punch test fixture was applicable for evaluating the behavior of 

multiple materials and structural components [ (McKeighan, 2007d), (2008a), (2008b)]. 

Figure 42. Simulation of the punch test on the thin TC128B plate material.

During testing, the actuator (actually, the punch frame) displacement was measured with a 

remote LVDT mounted on the actuator. Three string pots were attached to the backside (opposite 

the punch) surface of the test specimen. These three string pots were all in a line with the middle 

location in the center of the punch and the two outer locations at the circumferential periphery of 

the punch. This provided additional measurements of the backside deformation opposite the 

punch on the front of the panel. Load was also measured from the load cell on the servohydraulic test frame. Tests were performed in displacement control at an applied rate of 1 

inch/minute. The multiple data channels were recorded with a custom data acquisition system 

operating at 10 Hz. This typically provided total data files of anywhere from 500-2000 points.

The test series used for the validation of the TC128B constitutive and failure model was 

performed on 0.488-inch-thick plate specimens with various combinations of ram and manhole 

diameters (McKeighan, 2007d). The three tests performed used the 1.0, 1.5, and 2.0-inch 

diameter punches in combination with the 2.5, 3.0, and 3.5-inch diameter manhole covers, 

respectively. Photographs of the specimen failure behavior in these punch tests are shown in 
38 

Figure 43. In all cases, the punch test sheared out a plug of material with a diameter 

approximately equal to the punch diameter. 

An example of a model and simulation of a punch test on a 0.488-inch-thick TC128B plate is 

shown in Figure 44. The corresponding comparison of measured and calculated punch forcedisplacement curves for a series of three different tests on the TC128B plate is provided in 

Figure 45. In addition to the force-deflection curve the final profile of the plate specimens after 

the punch tests were digitized and compared to the analyses. A representative profile comparison 

is shown in Figure 46. 

Figure 43. Punch test failure mode for the thin TC128B plate material.

(a) Cross section of punch test geometry

(b) Punch test response

Figure 44. Simulation of the punch test on the thin TC128B plate material.
39 

Figure 45. Force-deflection curves for three punch test configurations on TC128B.

Figure 46. Comparison of the calculated and measured punch test plate profile.

The agreement of the measured and calculated behaviors for this punch test provides an 

additional validation that the BW failure model is appropriate for predicting puncture of the tank 

cars. The application of the failure model for assessing puncture energies for different tank 

geometries and impact conditions is provided in the following section of this report. 

2.5 Cryogenic 304 Stainless Steel Material Properties 

Assessing the puncture resistance of the DOT-113C120W9 tank car in LNG service requires the 

development of a constitutive model for the 304 stainless steel (SS) material at cryogenic LNG 

temperatures. A materials characterization testing program was previously performed for A240 
40 

304 SS at LNG temperatures (-260F, 110K) as part of the research supporting a Natural Gas Fuel 

Tender (NGFT) technical specification (Kirkpatrick, Wagner, & Northrup, 2019). This data is 

summarized here and applied to develop the constitutive model for 304 SS at LNG temperature

required for the DOT-113C120W9 LNG tank car analyses. 

Prior to performing the puncture assessment of the LNG tank car, the DOT-113C120W9 tank car 

puncture model was validated by analysis of the full-scale impact test on a DOT-113 tank car 

(Test 13) (FRA, 2022). This test was performed with liquid nitrogen as a surrogate lading at a 

colder cryogenic temperature (-321F, 77K). In preparation for this test, a corresponding series of 

material characterization tests was performed under FRA sponsorship at the colder liquid 

nitrogen cryogenic temperature (Wilson, Carolan, Trevithick, & Eshraghi, 2021). For analysis of 

the full-scale impact test, an additional material model was developed for the 304L stainless steel 

using this material data set. 

As part of the characterization test program for A240 304 SS at LNG temperatures (-260F, 

110K), tests of tensile and notched tensile behaviors were performed at quasistatic rates 

(0.0005/s) and tensile testing was performed at various elevated rates (0.01/s-10/s). Similarly, the 

test program on 304 SS at the colder Liquid Nitrogen cryogenic temperature (-321F, 77K)

included tensile and notched tensile tests performed at quasistatic rates (0.0005/s) and at various 

elevated rates (0.05/s-16/s). Both sets of data showed a trend where there were significant effects 

of strain rate between the quasistatic test rate (0.0005/s) and a relatively low strain rate of 0.05-

0.10/s. At higher rates there was much less strain rate sensitivity. As a result, three separate 

constitutive models were developed: 

1. A model for A240 304 SS at LNG temperatures (-260F, 110K) and quasistatic rate 

(0.0005/s). The model was developed at this strain rate since it was the only consistent set 

of tests including the notched tensile test required to develop the BW failure model. 

2. A model for A240 304 SS at LNG temperatures (-260F, 110K) and elevated rate (0.10/s). 

The model will be used in the evaluation of the puncture resistance for the DOT113C120W9 tank car in LNG service.

3. A model for A240 304 SS at liquid nitrogen cryogenic temperatures (-321F, 77K) and 

elevated rate (0.50/s). The model will be used in the evaluation of the full-scale impact 

Test 13 used to validate the puncture model for the DOT-113C120W9 tank car.

2.5.1 Constitutive Model for A240 304 SS at LNG Temperature

A characterization test program was performed on A240 304 stainless steel at LNG cryogenic 

temperature. The testing found that the behavior was similar to those used from literature sources 

for cryogenic 304L stainless steel [ (Kim, Kang, Kim, & Lee, 2012), (Blandford, Morton, Snow, 

& Rahl, 2007)]. Overall, the testing of the material produces strength and ductility properties that 

would result in a high puncture resistance for this material at cryogenic temperatures compared 

to other tank car steels. 

The material characterization test program included longitudinal and transverse tensile tests, 

notched round bar tensile tests, and longitudinal tensile tests at elevated strain rates. The 

objective was to perform three repeat tests at each condition to assess repeatability of results. The 

tensile data for the A240 304 at -260F and various strain rates is shown in Figure 47. The 
41 

quasistatic testing has a strain rate of approximately 0.0005 (in/in)/s. The elevated rate testing 

was performed using strain rates of 0.01, 0.1, 1.0, and 10.0 (in/in)/s. The testing was performed 

to ASTM E8/E8M − 16a standard test methods for tension testing of metallic materials using the 

specimen geometries shown in Figure 48 (Wakulchik, 2017). The stress-strain behaviors show a 

yield strength on the order of 100 ksi and an ultimate of approximately 195 ksi for the A240 304 

material at quasistatic rates. 

Figure 47. Comparison of the engineering tensile data for A240 304 SS at LNG 

temperature.

(a) ASTM E8 specimen geometry used in the quasistatic tensile testing

(b) Specimen geometry used in the elevated strain-rate testing

Figure 48. Specimen geometry used for the quasistatic and elevated strain-rate tensile tests.
42 

Increasing the loading rates results in an increase in the yield strength and a reduction in the 

ultimate strength. The elongation at the ultimate strength is similar for all the strain rates. The 

additional elongation after the ultimate stress for the high-rate tests is most likely a result of the 

smaller 0.5-inch gauge length in the high-rate tests compared to the 2.0-inch gauge length in the 

quasistatic tests. As a result, the necking behavior would produce a greater engineering 

elongation for the shorter gauge length measurements. At or above a loading rate of 0.1 (in/in)/s 

the stress-strain response is reasonably consistent. As a result, the tensile data at this rate was 

used to develop the constitutive model for the DOT-113 tank puncture analyses. 

Baseline Constitutive Model Development

The baseline constitutive model for the puncture performance assessment of the DOT-113 tank 

was developed based on testing of different samples of the A240 304 at -260F (110K) and a 

loading rate of 0.1 (in/in)/s. The model is developed by first converting the engineering stressstrain data to true stress and strain and then fitting these data with a piecewise linear curve, as 

shown in Figure 49. The procedure followed was previously described in Section 2.2. The 

resulting piecewise linear constitutive model was then applied to simulate the tensile test and 

compared back to the engineering data to confirm the material model properties. The model 

accurately reproduces the tensile behavior including necking and failure as shown in Figure 49. 

Figure 49. Constitutive model fit and tensile test validation for A240 304 SS at 110K

(0.10/s). 

The BW failure surface for the baseline model was adapted by using a previous BW failure 

surface for stainless steel and scaling the damage parameters proportionally to match the tensile 

test results. Normally, we would apply notched tensile tests to better define the shape of the BW 

failure surface. However, in this case, the notched tensile tests were performed on the material at 

the quasistatic loading rate instead of the elevated 0.1 (in/in)/s loading rate. To further investigate 

the potential effects of this assumed failure surface, a similar model was developed based on the 

quasistatic tensile data and applied to simulate the notched tensile test data. 
43 

Quasistatic Constitutive Model Development

The comparison of the quasistatic smooth tensile and notched tensile data for the A240 304 SS

material at LNG cryogenic temperature is shown in Figure 50. The drawings of the specimen 

geometries used in the notched tensile testing are shown in Figure 51. Since the notch increases 

the stress triaxiality in the gauge section it results in an increase in the yield and ultimate 

strength, as expected. The testing used a 1.0-inch gauge length extensometer bridging the notch, 

but the deformation will not be uniform within this gauge section due to the presence of the 

notch. As a result, the overall engineering elongation for these tests are reduced compared to the 

smooth round bar tension tests. However, the measured elongations of approximately 25 percent

are quite large for this type of testing on typical tank car steels. 

Figure 50. Summary of the 304 stainless quasistatic tensile test data at 110K (0.0005/s). 

The constitutive model for the investigation of the stress triaxiality effects was developed based 

on testing of different samples of the A240 304 at -260F (110K) and the quasistatic loading rate 

of 0.0005 (in/in)/s. The piecewise linear true stress-strain curve for the quasistatic material 

constitutive model was developed and applied to simulate the tensile test using the same 

approach as in the baseline model. The model accurately reproduces the tensile behavior 

including necking and failure as shown in Figure 52. 

The quasistatic constitutive model was then applied to investigate the performance of the model 

at various levels of confinement (stress triaxiality) by simulating the notched tensile tests. The 

comparison of the measured and simulated engineering stress-strain behaviors for the tensile and 

notched tensile tests are compared in Figure 53. The model is seen to match the shift in the 

stress-strain curves caused by the increase in stress-triaxiality but underpredict the failure loads 

and ductility of the notched tensile test. The comparison was considered to be acceptable since it 

would result in conservative estimates for failures in zones with elevated stress triaxiality. In 

addition, previous studies have shown that the punctures typically initiate at the inner surface of 

the tank with triaxialities that are similar to those in the tensile test. 
44 

Figure 51. Notched specimen geometries used in cryogenic stainless-steel testing.

Figure 52. Constitutive model fit and quasistatic tensile test validation for T304 SS at 110K

(0.0.005/s). 
45 

Figure 53. Constitutive model validation for quasistatic T304 SS at 110K (0.0005/s).

2.5.2 Constitutive Model for A240 304 SS at Liquid Nitrogen Temperature

The final constitutive model for A240 304 stainless steel was developed for the validation 

analysis of the full-scale impact test on a DOT-113 tank car (Test 13) (FRA, 2022) performed 

with liquid nitrogen as a surrogate lading at a colder cryogenic temperature (-321F, 77K). The 

material characterization tests were performed under FRA sponsorship at the colder liquid 

nitrogen cryogenic temperature (Wilson, Carolan, Trevithick, & Eshraghi, 2021). A comparison 

of the engineering stress-strain data for a range of strain rates is shown in Figure 54. The 

quasistatic loading rate was again 0.0005 (in/in)/s and the elevated rate testing was performed 

using strain rates of 0.05, 0.5, 5.0, and 16.0 (in/in)/s. As seen in the previous test series, 

increasing the loading rates results in an increase in the yield strength and for this test series a 

significant reduction in the ultimate strength. 

At the highest strain rates in this test series, the strain response is not smooth and a significant 

reduction in the strain levels during strain hardening and failure was observed. However, the 

corresponding comparison of the force-displacement behaviors, shown in Figure 55, show no 

indication of this effect. Therefore, the likely cause of the reduced stains at high loading rates is 

slipping of the extensometer and should be neglected. Comparisons of the stress-strain and forcedisplacement behaviors for the elevated rate data between 0.05 and 16 (in/in)/s show a relatively 

consistent behavior and strengths. Based on the responses measured, the data at 0.50 (in/in)/s. 

was selected for the constitutive model development. At this loading rate, good quality 

engineering stress-strain data measurement were still recorded. 

The constitutive model for the validation analyses of the full-scale Test 13 conditions was 

developed based on testing of different samples of the A240 304 at -321F (77K) and the loading 

rate of 0.50 (in/in)/s. The piecewise linear true stress-strain curve for the quasistatic material 

constitutive model was developed and applied to simulate the tensile test using the same 
46 

approach as in the baseline model. The model accurately reproduces the tensile behavior 

including necking and failure as shown in Figure 56. 

Figure 54. Engineering stress-strain data for T304 SS at 77K at different strain rates 

(Wilson, Carolan, Trevithick, & Eshraghi, 2021). 

Figure 55. Force-displacement data for T304 SS at 77K at different loading rates (Wilson, 

Carolan, Trevithick, & Eshraghi, 2021). 
47 

Figure 56. Constitutive model fit and tensile test validation for T304 SS at 77K (0.50/s). 
48 

3. Analysis of Different Size and Shape Impactors

3.1 Introduction and Background

In this section, the detailed BW failure model described in Section 2 is applied to assess various 

tank and head puncture conditions. The analyses in this section are focused on the two primary 

impact configurations studied in the NGRTC program of a normal side impact centered on the 

tank and an offset head impact with the impact point offset approximately 29 inches vertically 

downward from the center of the head. However, in this section we expand the range of 

impactors used in these scenarios to include a wide range of different sizes and shapes. 

3.1.1 Puncture Analysis Methodologies

The baseline failure models use a fine mesh of solid brick elements in the impact zone with an 

element dimension of approximately 0.040 inch (1 mm). The mesh transitions to shell elements 

outside the impact zone with increasingly mesh coarseness. The model of the commodity tank 

and BW impact zone mesh used in the tank shell puncture analyses is shown in Figure 57. An 

algorithm in LS-DYNA is used to tie the edge of the shell elements to the solid elements around 

the edge of the impact zone. 

As a result of the very fine mesh in the impact zone, the puncture models were significantly 

larger and have correspondingly longer run times. To allow for the evaluation of a wide range of 

impact conditions and tank geometries, some simplifications in the tank model were 

implemented. 

The first simplification was the use of symmetry planes. For the majority of side impact analyses 

described in this section, two symmetry planes were used to reduce the model to one-quarter of 

the full tank (a half model was used for the offset head impacts). This had a small effect since 

some tank car structural details could not be included in the quarter model (e.g., manway and 

bolsters). The primary effect of this approximation was that a side impact centered on the tank 

may have a slightly reduced stiffness for large dent sizes since the manway and surrounding 

structures are stiffer than the bare commodity tank. 

The head puncture modeling approach was identical to that of the tank side impact puncture 

analyses. The head impacts analyzed matched the NGRTC Test 1 impact condition (impact point 

offset below the tank head center). As a result, the problem had only 1 symmetry plane running 

vertically through the test specimen. This symmetry plane was used in most of the head impact 

simulations to reduce the model size by one half compared to the full head model. An example 

model of a tank head and BW impact zone mesh used in the head puncture analyses is shown in 

Figure 58. 

Another simplification in the tank puncture model was in the modeling approach used for the 

fluid lading. In the preliminary analyses an explicit model was used for the lading. However, this 

explicit model required a significant increase in the model size and was not ideally compatible 

with a quarter symmetry model. An alternate modeling approach was to smear the weight of the 

lading uniformly into the commodity tank wall. A comparison of the full tank car impact 

response using the two different lading modeling methodologies is shown in Figure 59. The 

comparison shows that the simplification of the smeared lading approach did not have a large 
49 

influence on the impact behavior. As a result, this approximation was applied for most analyses 

in this study. 

Figure 57. Tank model and impact zone mesh used for side impact puncture analyses.

Figure 58. Tank head model and impact zone mesh used for the head puncture analyses.
50 

Figure 59. Calculated tank car impact behavior using two different lading models.

The final geometric simplification of the impact modeling was that the ram car was not used in 

the analyses. Instead, a rigid model of the ram head was used with the mass of the entire ram car. 

This was a reasonable simplification since the measurements of ram car acceleration at 

distributed measurement locations were all in good agreement. 

Analysis of Tank Pressure Effects

The constant internal pressure modeling approximation used in the majority of the NGRTC 

analyses was found to introduce significant errors for larger impactor sizes. In the NGRTC 

chlorine tank car analyses the internal pressure was a constant 100 psi. However, with the 

formation of the dent in the tank during impact there will be an increasing hydrostatic internal 

pressure level. For the 6-inch impactor this increase in pressure was relatively small (10-15 

percent). However, the larger dents produced by the larger impactor sizes would result in a larger 

internal pressure increase. 

To demonstrate the influence of the variable internal pressure during the impact a series of 

analyses was performed. In these analyses, a control volume was established for the tank and the 

change in volume was used to calculate a corresponding change in pressure. The assumption in 

these analyses is that the tank has a 10.6 percent outage and the gas in the outage follows an ideal 

constant temperature compression behavior during impact. The resulting relationship between 

the relative volume and pressure in the tank is shown in Figure 60. 

The force-deflection curves with both constant and variable internal pressure for the 500 lb Cl 

tanks and the three different impactor sizes are shown in Figure 61. For the updated analyses 

with the variable pressure, the impact velocities were also reduced by 5 mph to be closer to the 

expected puncture threshold velocity. Adding variable pressure to the model results in a 

stiffening of the later portions of the force-deflection curve and a reduction in the ram 

displacements prior to the tank puncture. The reductions are more significant for the larger ram 

sizes. This is expected since the larger rams have larger displacements prior to the puncture with 
51 

a larger associated pressure change inside the tank. The comparisons show that the variable 

internal pressure does not have a significant influence on the puncture forces but does reduce the 

puncture energies by approximately 25-30 percent in the analyses with the 9x9 and 12x12 inch 

impactors. 

Figure 60. Pressure-volume relationship used for the tank control volume (10.6% outage). 

Figure 61. Effect of variable internal pressure on 500 lb tank impact response.

The control volume pressure histories for the three 500 lb Cl tank impact analyses are plotted as 

a function of the ram displacement in Figure 62. In the 6x6 inch impactor analysis the pressure 

change is less than 10 percent and the previous approximation of a constant 100 psi internal 

pressure is a reasonable simplification for the analyses. For the 9x9 and 12x12 inch impactors, 
52 

the internal pressures increase to approximately 120 psi and 140 psi, respectively, at the point of 

the puncture initiation. These pressure increases are becoming sufficiently large to influence the 

tank effective stiffness during the impact. 

The simulation of the NGRTC Test 2 impact conditions using the tank puncture model and 

variable internal pressure is shown in Figure 63. The model shown was reflected vertically about 

the symmetry plane (seen as a line in the figure) for improved visualization of the impact 

behavior. The impactor in this analysis was a rigid 6x6 inch ram with a 0.5-inch radius around 

the edges and a total weight of 286,000 lbs. The small rectangular patch of elements under the 

impactor (already punctured in Figure 63) is the fracture zone where the BW failure model was 

applied. The remainder of the tank structure was again modeled with 4-node shell elements and a 

tied shell-to-solid constraint was used at the interface of the two model regions. 

Figure 62. Calculated internal pressure variations in the 500 lb tank impact analyses.

Figure 63. Simplified tank model analysis with Bao-Wierzbicki failure assessment.
53 

The comparison of the measured and calculated force-deflection behavior for Test 2 with the 

tank puncture model is provided in Figure 64. The comparison shows overall good agreement 

between the calculation and test. The peak load at which the tank was punctured was very 

accurately captured by the model. The primary discrepancy of the test and model was a slightly 

more compliant behavior in the model at large displacements. This difference in compliance 

could primarily be attributed to the removal of the manway from the tank model. 

Figure 64. Comparison of the calculated and measured Test 2 impact and puncture 

behavior. 

3.2 Side Impact Analysis of Different Size and Shape Impactors

The tank puncture model was used to assess the puncture energies for a wide range of impactor 

sizes and shapes. The tank design used in these analyses is the 105J600 chlorine tank car. The 

TC128B tank shell is 100 inches in diameter and 472 inches long with 2:1 ellipsoidal heads. The 

tank is covered by a 0.119-inch-thick A1011 jacket with a 4-inch standoff from the tank. 

An example puncture response is shown in Figure 65. The analysis shown corresponds to the 600 

lb Cl tank geometry (note: the 600 lb tank designation is used in the industry and refers to a tank 

with a 600-psi test pressure). The ram head model was updated in these analyses to include the 

tapered geometry used in the full-scale testing and an updated weight of 295,000 lbs. The tapered 

geometry included a 6x6 inch contact face but flared out to duplicate the ram geometry in the 

impact tests of the NGRTC program. Although the ram head was tapered in the analyses, the 

contact patch remained the 6x6 inch face until the protective layers and/or tank were punctured. 

As a result, the tapered geometry did not play a significant role in the prediction of the puncture 

energies reported in this report. 

The progression of the fracture behavior in the BW failure patch is shown in Figure 66. The 

fracture initiated near the corners of the impactor and propagated initially along the side of the 

impactor face. The crack subsequently ran along the top and bottom of the ram face. 
54 

The energy balance for the 600 lb chlorine car impact is shown in Figure 67. The initial impact 

energy is approximately 4 million ft-lbs (all in the kinetic energy). As the impact progresses, the 

ram is decelerated, and the kinetic energy drops off. The energy transfer is from the kinetic 

energy of the ram to the internal energy of the tank (plastic deformations of the tank material) 

and the pressure-volume work caused by the indentation reducing the total tank volume. The 

internal energy of the tank at rupture is approximately one million ft-lbs and the pressure volume 

work is between 500,000 and 600,000 ft-lbs. The hourglass energy and sliding energy in the 

calculation are both negligible indicating that the calculation is stable and does not have any 

numerical energy losses. 

Figure 65. Detailed impact and puncture sequence for a 600 lb chlorine car.
55 

Figure 66. Calculated puncture initiation and fracture progression.

Figure 67. Calculated energy balance for the 600 lb chlorine tank car impact (R10F).

3.2.1 Effects of Impactor Size and Shape

A potential concern is that the selection of the 6x6 inch ram, as the primary threat used in the 

NGRTC program, will not identify the protection concept that provides the greatest benefit for 

impacts with a wide range of impactor types. To evaluate the effects of the ram impactor size and 

shape, analyses were performed on the 600 lb chlorine tank car being impacted by a range of 

impactors. 

The first set of analyses used 3x3, 3x6, 6x6, 9x9, 12x12, 3x12, 12x3 rectangular impactors, all 

with a 0.50-inch radius around the edges. The models for the tank were similar but with changes 

in the BW impact zone to match the corresponding impactor face shape and size. The model of 

the commodity tank and BW impact zone mesh used in the 12x12 inch impactor analyses is 

shown in Figure 68. Again, the refined zone is maintained along the perimeter of the impactor 

face with a characteristic element dimension of approximately 0.040 inch (1 mm). 
56 

Figure 68. Tank model and impact zone mesh used for the 12x12 inch impactor.

The initial set of shell puncture analyses were performed with the square impactors. The models 

for the square impactors are shown in Figure 69. The comparison of the force-deflection 

behaviors and puncture energies with the 3x3-inch, 6x6-inch, 9x9-inch, and 12x12-inch square 

impactors is shown in Figure 70 (the puncture energy is obtained by integrating the forcedeflection curve of the impact up to the point of the tank puncture). Note that higher impact 

speeds are used in the calculations as the impactor size is increased to achieve the higher 

puncture energies required. Since the impact behavior is relatively insensitive to impact speed 

(within a limited range), the impact velocities were not considered to be a significant factor in 

the comparison. 

The calculated puncture behaviors in Figure 70 show progressively increasing puncture forces 

and puncture energies with increasing impactor size. Figure 71 shows a plot the puncture force 

for all the square impactor analyses correlated to the impactor perimeter length. The puncture 

forces show a nearly linear correlation with the ram perimeter length which is consistent with the 

punch shear failure mechanisms described in Section 1.3. The failure behavior can also be seen 

by the puncture of the ram through the tank shell BW impact zone as shown for the 3x3 and 

12x12 inch impactors in Figure 72. Similar failure behaviors were seen for the 6x6 and 9x9 inch 

impactors. All the impactors punch out a section of the tank wall approximately equal in size and 

shape to the impactor face. 

The second set of tank impact analyses performed used rectangular impactor face profiles to 

investigate the effects of the impactor aspect ratio. The additional impactors used were a 3x6, 

3x12, and 12x3 impactors as shown in Figure 73. The results from these impact analyses are 

added to the puncture force versus ram perimeter length graph reproduced in Figure 74. The 3x6 

impactor agrees well with the original linear correlation for the square impactors. However, the 
57 

3x12 and 12x3 impactors both puncture at a force level that is 100-200 kips below the linear 

correlation. 

 

(a) 3x3 impactor (b) 6x6 impactor

 

(c) 9x9 impactor (d) 12x12 impactor

Figure 69. Models of the different size square impactors.

Figure 70. Updated 600 lb tank impact analysis with different size impactors.
58 

Figure 71. Puncture forces for the 600 lb tank impacts with different size impactors.

Figure 72. Calculated puncture behaviors (3x3 and 12x12 inch Impactors).
59 

(a) 3x3 impactor (b) 3x6 impactor

(c) 3x12 impactor (d) 12x3 impactor

Figure 73. Models of the different size rectangular impactors.

Figure 74. Puncture forces for the 600 lb tank impacts with different size impactors.

The calculated damage development in the tank wall prior to puncture is shown for the 3x3, 3x6, 

3x12, and 12x3 inch impactors in Figure 75. An examination of the damage profiles explains the 
60 

reduction of the puncture force levels for the 12x3 and 3x12 impactors relative to the linear 

correlation. All the analyses develop stress concentrations and increased damage at the corners. 

However, for the larger aspect ratio impactors, the discrepancy is much larger between the 

maximum loading and damage at the corners and at the minimum locations along the middle of 

the long edges of the impact face. Thus, the long edges of the impactor do not effectively 

contribute to the puncture force resistance and the high aspect ratio impactors behave as if they 

were effectively smaller. 

The third set of tank impact analyses performed used round impactor face profiles to investigate 

the effects of the impactor shape. The additional impactors used were a 5.73-, 7.64-, 9.55-, 

11.46-, and 13.37-inch diameter impactors (ram face perimeter lengths of 18, 24, 30, 36, and 42 

inch, respectively), as shown in Figure 76. The results from these impact analyses are added to 

the puncture force versus ram perimeter length graph reproduced in Figure 77. All the round 

impactor analyses predict puncture at a force level that is approximately 200 kips above the 

linear correlation. 

(a) 3x3 impactor (b) 3x6 impactor

(c) 3x12 impactor (d) 12x3 impactor

Figure 75. Calculated puncture behaviors (3x3 and 12x12 inch Impactors).
61 

(a) 5.73-inch-diameter (b) 7.64-inch-diameter (c) 9.55-inch-diameter

(d) 11.46-inch-diameter impactor (e) 13.37-inch-diameter impactor

Figure 76. Models of the different size round impactors.

Figure 77. Puncture forces for the 600 lb tank impact analyses with different size and shape 

impactors.

The calculated damage development in the tank wall prior to puncture is shown for the 5.73- and 

13.37-inch diameter impactors in Figure 78. An examination of the damage profiles explains the 

increase for the puncture force levels for the round impactors relative to the linear correlation. 

The round impactor analyses have very uniform loads and damage development around the 
62 

impact face perimeter with no significant stress concentrations. Thus, the round shape of the 

impactors maximizes the contribution of the entire perimeter to the puncture force resistance. 

(a) 5.73-inch-diameter impactor (b) 13.37-inch-diameter impactor

Figure 78. Calculated puncture behaviors for different size round impactors. 

3.2.2 Definition of the Impactor Characteristic Size 

A summary of the above analyses of side impact puncture behaviors for various size and shape 

impactors is provided in Table 2. The analyses show that the puncture force is strongly tied to the 

size of the impactor but also has a secondary influence of the impactor shape. The round 

impactors avoid any stress and strain concentrations that might occur at the corners of the 

rectangular impactors and therefore require a higher force to puncture the wall for an equivalent 

impactor face perimeter length. Similarly, the higher aspect ratio rectangular impactors 

accentuate the stress concentration effects and further reduce the puncture force compared to the 

square impactors. 

These secondary effects of the impactor shape suggest that there is potentially an improved 

measure of the impactor effective size that might better capture these secondary shape effects. 

The parameter developed that best captured these effects was to define the impactor 

“characteristic size” as the square root of the area of the impactor face. For a square impactor the 

characteristic size is equal to the length along the edge of the impact face (i.e., the 6x6 inch 

impactor has a 6-inch characteristic size). For round impactors, the characteristic size is 

approximately 11 percent smaller than the diameter. For high aspect ratio impactors, the 

characteristic size is smaller than the average length of the perimeter sides. For example, the 

3x12 impactor has a perimeter length that is 25 percent larger than that for the 6x6 inch impactor. 

However, the 6x6 inch impactor and the 3x12 impactor both have the same characteristic size of 

6 inches. 
63 

Table 2. Summary of the baseline side impact analyses for the 105J600 tank car

Calculation Tank 

Type 

Tank 

Shell 

Shell 

Jacket 

Impact 

Conditions

Internal 

Pressure

(psi)

Puncture 

Force (lbs)

Puncture 

Energy 

(ft-lbs)

R15D 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

15 mph

6”x6” ram 100 psi 1.167E+06 1.500E+06 

R15E 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

25 mph

12”x12” ram 100 psi 2.160E+06 5.800E+06 

R15F 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

20 mph

9”x9” ram 100 psi 1.690E+06 3.940E+06 

R11G 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

10 mph

3”x3” ram 100 psi 5.760E+05 4.050E+05 

R11H 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

25 mph

3”x12” ram 100 psi 1.235E+06 1.950E+06 

R11I 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

25 mph

12”x3” ram 100 psi 1.280E+06 2.360E+06 

R11M 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

25 mph

5.73 in. dia. 100 psi 1.044E+06 1.000E+06 

R11N 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

25 mph

13.37 in. dia. 100 psi 2.203E+06 6.040E+06 

R11O 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

25 mph

9.55 in. dia. 100 psi 1.567E+06 3.000E+06 

R11Q 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

15 mph 

5.73 in. dia. 100 psi 1.025E+06 1.300E+06 

R11T 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

15 mph

3”x6” ram 100 psi 8.505E+05 8.350E+05 

R11U 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

20 mph

7.64 in. dia. 100 psi 1.343E+06 2.180E+06 

R11V 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

25 mph

11.46 in. dia. 100 psi 1.894E+06 3.950E+06 

The summary of the puncture forces for the various impactors, shown in Figure 78, is 

regenerated using the impactor characteristic size in Figure 79. The figure shows that the 

impactor characteristic size parameter provides a much closer correlation for all the impactor 

sizes and shapes analyzed. Overall, there is a strong linear correlation of the puncture force with 

the characteristic size of the impactor. 

A similar summary of the puncture energies for the various impactors is shown in Figure 80. The 

figure shows that the impactor characteristic size parameter also correlates well to the puncture 

energies. There is more scatter in the correlation of the puncture energies but that is expected 

since various factors such as the impact speed and BCs have been shown to introduce variations 

in the calculated impact energy. The impact energies in Figure 80 show that the correlation is 

roughly with the square of the characteristic size of the impactor. This is a result of the linear 

increase in the puncture force combined with a similar increase in the displacements required to 

reach the impact force. 
64 

Figure 79. Correlation of the puncture forces with ram characteristic size.

Figure 80. Correlation of the puncture energies with ram characteristic size.

3.2.3 Analysis of Impactor Edge Sharpness

The impactor models used in the above analyses all had a 0.5-inch-radius edge around the face of 

the impactor. This value was originally selected to match the edge conditions on the 6x6 inch 

impactor used in the NGRTC testing and analyses (Kirkpatrick, 2009a). The edge radius was a 

simplification that would eliminate effects such as the edge deformation and wear for repeated 

use of the impactor in testing and was expected to produce more repeatable impact behaviors. In 

this section, the effect of the edge radius was analyzed to quantify the importance of the impactor 

edge sharpness. 
65 

The analyses performed used the 3x3, 3x12, and 12x12 inch impactors. These were selected to 

include the smallest, largest and highest aspect ratio of the impactors studied with the assumption 

that these would be the cases where the edge radius might be the most significant. The analyses 

were performed for all three impactors with the original 0.5-inch edge radius as well as a much 

sharper 0.1-inch edge radius. In addition, an analysis using the 12x12 inch impactor with a large 

1.0-inch edge radius was also performed. 

A summary of the results for these side impact analyses with different impactor face edge radii is 

listed in Table 3. The corresponding force deflection curves for all the analyses are shown in 

Figure 81. The comparisons show that the edge radius has a small effect on the overall response 

and calculated puncture forces and energies. The largest discrepancy was for the puncture 

energies with the 3x12 impactor where the 0.1-inch edge radius resulted in a 10 percent

reduction in the puncture energy compared to the baseline 0.5-inch radius. However, this 

difference was probably influenced by the fact that the puncture occurred in a very flat region of 

the force-deflection response for this impact scenario. The comparison of the corresponding 

puncture forces for these two 3x12 impactor analyses show that they agree to within 

approximately 1 percent. 

Table 3. Summary of the analyses to assess the impactor face edge radius.

Impact 

Calc. 

Tank 

Type 

Tank 

Shell

Tank 

Jacket 

Impact 

Conditions

Impactor 

Edge 

Radius

Internal 

Pressure

(psi)

Puncture 

Force 

(lbs)

Puncture 

Energy 

(ft-lbs)

R11G 600 lb 

Cl 

0.981 in

TC128B 

0.119 in

A1011 

10 mph

3”x3” ram 0.50 inch 100 psi 576,000 405,000 

R11J 600 lb 

Cl 

0.981 in

TC128B 

0.119 in

A1011 

10 mph

3”x3” ram 0.10 inch 100 psi 590,000 375,000 

R11H 600 lb 

Cl 

0.981 in

TC128B 

0.119 in

A1011 

25 mph

3”x12” ram 0.50 inch 100 psi 1,235,000 1,950,000 

R11K 600 lb 

Cl 

0.981 in

TC128B 

0.119 in

A1011 

25 mph

3”x12” ram 0.10 inch 100 psi 1,227,000 1,750,000 

R15E 600 lb 

Cl 

0.981 in

TC128B 

0.119 in

A1011 

35 mph

12”x12” ram 0.50 inch 100 psi 2,160,000 5,800,000 

R11P 600 lb 

Cl 

0.981 in

TC128B 

0.119 in

A1011 

35 mph

12”x12” ram 0.10 inch 100 psi 2,006,000 5,700,000 

R12V 600 lb 

Cl 

0.981 in

TC128B 

0.119 in

A1011 

35 mph

12”x12” ram 1.00 inch 100 psi 2,206,000 5,780,000 
66 

Figure 81. Calculated force-deflection behaviors for the impactor edge radii evaluations. 

The calculated puncture response for the two analyses with the 3x12 inch impactors is shown in 

Figure 82. The calculated response is shown at times of 80 and 100 ms after impact 

corresponding to points after the fracture initiation and full penetration of the impactor through 

the tank wall. The comparison shows that the 0.1-inch impactor puncture development is further 

along at a time of 80 ms and results in a slightly cleaner fracture surface around the final plug 

formation at 100 ms. However, these differences were minor, and the dominating punch-shear 

failure mechanism is seen for all the analyses. As a result, the edge radius is considered to be a 

secondary effect for the puncture of the pressure tank cars. 
67 

(a) 0.5-inch radius (t=80 ms) (b) 0.5-inch radius (t=100 ms)

(c) 0.1-inch radius (t=80 ms) (d) 0.1-inch radius (t=100 ms)

Figure 82. Calculated puncture behavior for the 3x12impactor with 0.5- and 0.1-inch edge 

radii.

3.2.4 Analysis of Complex Impactor Shapes

The above analyses of the effects of impactor sizes and shapes considered only idealized 

rectangular and round impactors. However, in more general derailment and impact conditions, 

the impactors may have a much more complex geometry or impact condition. In this section, we 

analyze the impact behavior for some of these complex impactor scenarios. 

Rail Section Impactor

One significant impactor threat that has been observed in derailments is a section of broken or 

displaced rail. To evaluate this threat, a rail section impactor was created and used to calculate 

the puncture behavior. The impactor model created is shown in Figure 83. The impactor is a

section of 141-pound rail with a flat end impactor face. The geometry used to generate the rail 

section impactor is shown in Figure 84. 
68 

Figure 83. Model for the rail section impactor.

To compare the puncture behavior to other impactor shapes, we need to evaluate the 

characteristic size of the rail section impactor. However, for this impactor with a mix of concave 

and convex curves around the perimeter of the impact face the impactor area can be defined by 

different methodologies. The first is to use the cross-sectional area of the rail as shown in Figure 

84(a). This cross-sectional area is 13.8 square inches which corresponds to an impactor 

characteristic size of 3.7 inches. The second methodology would be to use the bounding impact 

area defined in Figure 84(b). This bounding impact area is 33.4 square inches and corresponds to 

an impactor characteristic size of 5.8 inches. 
69 

(a) Cross section geometry

(b) Cross section and bounding area definition

Figure 84. Geometry for the rail section impactor.
70 

The calculated side impact puncture behavior for the rail section impactor is shown in Figure 85. 

The damage is greatest at the stress concentrations at the corners of the head and base of the rail 

and the puncture initiates at these sites. The puncture then progresses to the point that a rail 

shaped plug of material is removed from the tank wall. 

(a) Before puncture (b) Puncture initiation

(c) Complete puncture (d) Tank puncture mode

Figure 85. Calculated side impact puncture behavior for the rail section impactor.

The calculated side impact puncture force for the rail impactor is compared to the other 

impactors in Figure 86. The rail puncture force is shown using both the 3.7- and 5.8-inch initial 

estimates for the impactor characteristic size. The comparison in Figure 86 shows that these 

estimates for the characteristic size bound the correlation for the other simple impactor 

geometries. If we use the fit from the previous analyses, the rail impactor puncture force 

corresponds to an impactor with a 5-inch characteristic size. 
71 

Figure 86. Puncture forces for the 600 lb tank impact analyses with the rail impactor.

Coupler Impactor

A second significant impactor threat that has been observed in derailments is a coupler. To 

evaluate this threat, a coupler impactor model was created and used to calculate the puncture 

behavior. The impactor model created is shown in Figure 87. It is a rigid model of the coupler 

head and shank with the complex impactor face geometry. 

Figure 87. Model for the coupler head impactor. 
72 

As a result of the complex impactor face profile of the coupler, it was not possible to estimate the 

characteristic size in advance. As a result, the impact and puncture analyses were performed, and 

the calculated puncture behaviors were used to back calculate the equivalent characteristic size 

of the impactor. 

The initial coupler impact analysis was performed using a normal side impact scenario with an 

initial impact velocity of 25 mph and an impactor weight of 295,000 lbs. The calculated coupler 

impact damage development and puncture behavior is shown in Figure 88. The calculated 

damage profile shows that the damage development is nonuniform over the impact face of the 

coupler with the largest concentration of damage around the protruding interlocking lug on the 

wing with secondary concentrations around the knuckle. These load concentrations are 

significant since the damage under the interlocking lug initiates a crack through the tank shell 

significantly earlier than the load at which the entire coupler head punctures the tank. 

The calculated force-deflection behavior for the coupler normal side impact is compared to that 

of the 12x12 impactor in Figure 89. The comparison shows that the force deflection behaviors 

for the complete puncture are very similar with a peak force of approximately 3 million pounds 

and a maximum ram displacement of 55-60 inches. However, the fracture initiation under the 

interlocking lug occurs at a load of approximately 1.7 million pounds and a ram displacement of 

40 inches. Thus, the point at which the commodity release would occur is significantly earlier for 

the coupler normal impact than for the 12x12 inch impactor. 

The nonuniformity of the loading and damage suggests that the coupler impact and puncture 

behavior could be very sensitive to the orientation of the coupler head relative to the tank wall. 

To investigate this effect, two additional calculations were performed where the coupler head 

orientation was rotated laterally in each direction by 15 degrees. The motion of the rotated 

impactors is still in a direction normal to the tank wall. 

The calculated impact damage and force deflection for the first rotated coupler impact are shown 

in Figure 90 and Figure 91, respectively. The rotation for this case results in a more concentrated 

load on the coupler interlocking lug and the tank wall in initially breached at a force of 

approximately 1 million pounds and an impact energy of 800,000 ft-lbs. 
73 

(a) Before puncture (t=60 ms)

(b) Puncture initiation (t=120 ms)

(c) Complete puncture (t=220 ms)

Figure 88. Calculated puncture behavior for the coupler head normal impact.
74 

Figure 89. Calculated force-deflection behavior for the coupler head normal impact.

(a) Before puncture (t=20 ms)

(b) Puncture initiation (t=40 ms)

(c) Puncture growth (t=100 ms)

Figure 90. Calculated puncture behavior for the coupler head 15-degree rotation impact.
75 

Figure 91. Calculated force-deflection behavior for the coupler 15-degree rotation impact.

The calculated impact damage and force deflection for the second rotated coupler impact 

configuration are shown in Figure 92 and Figure 93, respectively. The rotation for this case

produces a more distributed load across the coupler face. The tank wall is not breached until 

reaching a force of approximately 2.3 million pounds and an impact energy of 5.7 million ft-lbs. 

The forces for which the tank wall is breached in the three coupler impact scenarios are added as 

the horizontal dashed lines in Figure 94. Using the correlation between puncture force and 

impactor characteristic size developed in the previous analyses with the idealized impactors, we 

can calculate the effective size of the coupler in these three impact analyses. This methodology 

shows that in the unfavorable orientation the coupler head has the puncture potential of a 5-inch 

characteristic size impactor (e.g., a 5x5 inch impactor). However, at a more favorable 

orientation, the coupler head has a similar puncture potential to the 12x12 inch impactor (12-inch 

characteristic size). 
76 

(a) Before puncture (t=120 ms)

(b) Puncture initiation (t=180 ms)

(c) Puncture growth (t=200 ms)

Figure 92. Calculated puncture behavior for the coupler -15-degree rotation impact.
77 

Figure 93. Calculated force-deflection behavior for the coupler -15-degree rotation impact.

Figure 94. Puncture forces for the 600 lb tank impact analyses with the coupler head 

impactor.

3.2.5 Analysis of Impactor Orientation Effects

The above analysis of the coupler head impacts at various orientations show that the orientation 

of an impactor can play a significant role on the puncture response. To quantify this effect, the 

12x12 inch impactor with a 0.1-inch edge radius was used in a series of analyses where the 

orientation was varied. The orientation included various combinations of yaw and pitch rotation 

of the impactor head. Examples of the impact scenarios for various impactor yaw rotation are 
78 

shown in Figure 95. The impact condition for all the analyses was still a normal velocity 

trajectory with a 25-mph impact speed and a total impactor weight of 295,000 lbs. 

The calculated force-displacement curves and integrated puncture energies for the analyses with 

various levels of yaw rotation are shown in Figure 96. The figure shows that all the analyses are 

following along a roughly equivalent characteristic force-deflection curve for the tank and 

impact conditions. However, as the yaw rotation increases, the concentration of impact load and 

damage along the leading edge of the impactor increases and the point at which the impactor 

punctures the tank is earlier (lower force levels). 

(a) 15-degree yaw rotation (b) 30-degree yaw rotation (c) 45-degree yaw rotation

Figure 95. Example impactor orientation analyses performed for side impacts.

Figure 96. Calculated force-deflection behaviors for the 12x12 inch impactor and various 

levels of yaw rotations.
79 

A summary of all the analyses performed to quantify the impactor orientation effects is provided 

in Table 4. Similarly, the puncture forces for all the analyses are plotted against the impactor 

rotation angles in Figure 97. The effects for the pitch rotation are similar to those for the yaw 

rotation, but with a slight increase in the puncture forces resulting from the relative stiffness of 

the tank for bending in the longitudinal and radial directions in the impact zone. The analyses 

where the yaw rotation was maintained at 45 degrees then various levels of pitch rotation were

added further concentrates the load and damage at the corner of the impactor. The damage 

profiles for the edge and corner impacts produced by the extreme rotation combinations analyzed 

are shown in Figure 98. 

Table 4. Summary of the analyses to assess the impactor orientation effects.

Side Impact 

Calculation

Tank 

Type

Tank 

Shell

Tank 

Jacket 

Impact 

Conditions

Ram 

Yaw 

Angle 

(deg.)

Ram 

Pitch 

Angle 

(deg.)

Puncture 

Force (lbs)

Puncture 

Energy

(ft-lbs)

R11P 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 0.0 0.0 2.154E+06 5.650E+06 

R12H 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 5.0 0.0 1.910E+06 3.950E+06 

R12I 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 10.0 0.0 1.576E+06 3.100E+06 

R12J 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 15.0 0.0 1.348E+06 2.250E+06 

R12K 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 20.0 0.0 1.130E+06 1.150E+06 

R12L 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 45.0 0.0 8.380E+05 5.850E+05 

R12O 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 45.0 5.0 8.160E+05 5.400E+05 

R12P 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 45.0 10.0 7.850E+05 4.800E+05 

R12Q 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 45.0 15.0 7.400E+05 4.250E+05 

R12R 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 45.0 20.0 6.510E+05 3.300E+05 

R12S 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 45.0 45.0 9.096E+05 7.000E+05 

R13C 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 0.0 5.0 2.020E+06 5.400E+06 

R13D 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 0.0 10.0 1.830E+06 3.900E+06 

R13E 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 0.0 15.0 1.613E+06 3.400E+06 

R13F 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 0.0 20.0 1.423E+06 2.900E+06 

R13G 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 0.0 45.0 1.090E+06 1.150E+06 
80 

Figure 97. Puncture forces for the 12x12 inch impactor at various orientations.

For comparison, the puncture forces calculated for the rotated 12x12 inch impactor were 

converted to obtain the impactor characteristic size which is shown on the right axis of Figure 

97. The plot shows that the characteristic size of the impactor decreases rapidly as the rotation 

increases from 0 to approximately 30 degrees then levels out beyond that point where the contact 

is primarily with only the edge or corner of the impactor. The characteristic size of the 12x12

impactor drops from 12 inches in the normal impact to approximately 4.5-5 inches in an edge 

impact. The characteristic size is further reduced to approximately 3 inches for the corner impact. 

These results show that impacting objects with corners and edges can have the penetration 

potential of a much smaller object if the orientation of the impactor concentrates the loading to 

the edge or corner. 
81 

(a) Normal impact (no rotation) (b) 45-deg yaw and 0-deg pitch

(c) 0-deg yaw and 45-deg pitch (d) 45-deg yaw and 45-deg pitch

Figure 98. Puncture behavior for the 12x12 inch impactor with face, edge, and corner 

impacts.
82 

3.3 Head Impact Analysis of Different Size and Shape Impactors

The above sections describe the effects of different size and shape impactors on the side impact 

behavior and puncture response. A similar set of analyses were performed for the head impact on 

the 600 lb tank car. The head impact analyses were performed using a configuration similar to 

the head impact tests in the NGRTC program (Kirkpatrick, 2009a). The head and a short length 

of the tank shell are used, and the boundary condition is a rigid restraint at the trailing edge of the 

shell. This boundary condition is representative of the head impact test frame used in the 

NGRTC program.

The heads were impacted by various size impactors. In the analyses, the impactor is given an 

initial velocity and constrained to move in the longitudinal direction only. The target impact 

point was offset approximately 29 inches vertically downward from the center of the head. The 

weight of the impactor is 295,000 lbs which matches the final impactor test sled weight used in 

the NGRTC tests. The primary difference from the NGRTC head test series is that the heads 

were pressurized to 100 psi in the analyses performed in this section. For these preliminary 

analyses a constant internal pressure level is used. The constant pressure assumption is more 

appropriate for the head impacts where the structural stiffness of the head geometry is larger 

(thus pressure effects play a smaller role). In addition, the dent shape for head impacts is a 

smaller fraction of the tank volume than the side impact dent shape and the pressure change is 

smaller. 

3.3.1 Effects of Impactor Size and Shape

An example of the calculated impact and puncture behavior for the 600 lb tank head is shown in 

Figure 99. The specific example shown is for the 11-mph impact with the 6x6 inch impactor. The 

response mechanisms include a dent formation under the impactor for both the tank head and 

head shield, buckling of the jacket supporting the head shield, and eventually the puncture of the 

head and shield. The puncture initiates at the top edge of the impactor and opens a flap of 

material under the impact face. 

A summary of results from the baseline head impact analyses is provided in Table 5. All the

analyses in the table are for the 600 lb tank geometry with a 0.5-inch-thick A572-50 head shield 

and 100 psi internal pressure. The impactors all have the baseline 0.5-inch edge radius. The 

calculated force-deflection behaviors and puncture energies for the 3x3, 6x6, 9x9, and 12x12 

inch impactors are shown in Figure 100. The highly constrained head structures result in a 

behavior where the impact force is roughly linearly proportional to the impactor displacement 

(dent depth). 

The calculated head impact puncture forces are plotted against the impactor characteristic size in 

Figure 101. The puncture forces again show a trend of a linear correlation with the impactor 

characteristic size, with slightly more scatter in the correlation. It is believed that this is a result 

of the offset impact condition that produces uneven loading at the upper and lower edges of the 

impactor. As a result, the results are more sensitive to the shape of the impactor. 
83 

 

(a) Impact configuration (b) Puncture behavior

Figure 99. Analysis of the tank head puncture behavior for the 6x6 inch impactor.

Table 5. Summary of the baseline head impact analyses. 

Head Impact 

Calculation

Tank 

Type

Tank 

Head

Jacket 

or Head 

Shield

Impact 

Conditions

Impactor 

Edge 

Radius

Internal 

Pressure

(psi)

Puncture 

Force (lbs)

Puncture 

Energy

(ft-lbs)

R10K 600 lb Cl 1.1360 

A516-70

0.500” 

A572-50

14 mph

6”x6” ram 0.50 inch 100 psi 1,206,000 1,121,000 

R10N 600 lb Cl 1.1360 

A516-70

0.500” 

A572-50

11 mph

6”x6” ram 0.50 inch 100 psi 1,229,000 1,110,000 

R10V 600 lb Cl 1.1360 

A516-70

0.500” 

A572-50

20 mph

9”x9” ram 0.50 inch 100 psi 1,868,000 2,450,000 

R11F 600 lb Cl 1.1360 

TC128B 

0.500” 

A572-50

25 mph

12”x12” ram 0.50 inch 100 psi 2,334,000 3,672,000 

R11L 600 lb Cl 1.1360 

TC128B 

0.500” 

A572-50

10 mph

3”x3” ram 0.50 inch 100 psi 774,000 400,000 

R11M 600 lb Cl 1.1360 

TC128B 

0.500” 

A572-50

18 mph

3”x12” ram 0.50 inch 100 psi 1,298,000 1,035,000 

R11N 600 lb Cl 1.1360 

TC128B 

0.500” 

A572-50

18 mph

12”x3” ram 0.50 inch 100 psi 1,660,000 1,830,000 

R11O 600 lb Cl 1.1360 

TC128B 

0.500” 

A572-50

12 mph

5.73” Dia. 0.50 inch 100 psi 1,176,000 915,000 

R11P 600 lb Cl 1.1360 

TC128B 

0.500” 

A572-50

18 mph

9.55” Dia. 0.50 inch 100 psi 1,753,000 2,000,000 

R11R 600 lb Cl 1.1360 

TC128B 

0.500” 

A572-50

15 mph

7.64” Dia. 0.50 inch 100 psi 1,562,000 1,520,000 

R11S 600 lb Cl 1.1360 

TC128B 

0.500” 

A572-50

21 mph

11.46” Dia. 0.50 inch 100 psi 2,236,000 3,500,000 
84 

Figure 100. Calculated head impact force-deflection behaviors for the square impactors.

Figure 101. Calculated head impact puncture forces for various impactors.

The largest discrepancy from the linear puncture force correlation was for the 12x3 inch 

impactor that has a puncture force significantly larger than the fit to the data. The damage 

development and puncture behavior for the 12x3 and 3x12 inch impactors are shown in Figure

102. The comparison shows that the load is distributed over a much wider region for the 12x3 

impactor and as a result it acts like a larger impactor compared to the 3x12 impactor for this 

scenario. Therefore, the 12x3 impactor orientation had a small sensitivity to the offset impact 

effects and the 3x12 impactor had a large sensitivity to the offset impact geometry.
85 

(a) 3x12 impactor (t=60 ms) (b) 3x12 impactor (t=80 ms)

(c) 12x3 impactor (t=80 ms) (d) 12x3 impactor (t=100 ms)

Figure 102. Calculated head puncture behaviors for the 3x12 and 12x3 impactors.

The calculated head impact puncture forces and energies are compared to the corresponding side 

impact values in Figure 103 and Figure 104, respectively. The head puncture forces are on 

average approximately 10 percent greater than the side impact puncture forces. The difference is 

a combination of two competing factors. First the combined head and head shield thickness is 

almost 50 percent thicker than the combined thickness of the tank shell and jacket. However, this 

thickness increase is partially negated by the offset head impact scenario producing larger stress 

and strain concentrations at the top edge of the impactor that reduce the puncture forces. 

The comparison of the side and head puncture energies in Figure 104 show that again the head 

impacts have a similar fit to the square of the ram characteristic size, but the puncture energies 

are 30 to 35 percent lower for the head than for the shell. The difference is primarily that the 

head and rigidly constrained impact scenario are much stiffer than for the shell side impacts. As 

a result, the puncture forces are reached at significantly lower ram displacements resulting in the 

reduction of puncture energies. 
86 

Figure 103. Comparison of the calculated head and side impact puncture forces.

Figure 104. Comparison of the calculated head and side impact puncture energies.

3.3.2 Analysis of Complex Impactor Shapes

The above analyses of the effects of impactor sizes and shapes considered only idealized 

rectangular and round impactors. However, in more general derailment and impact conditions, 

the impactors may have a much more complex geometry or impact condition. In this section, we 

analyze the head impact behavior for complex impactor scenarios. 
87 

Rail Impactor

The calculated head deformations for an 11-mph impact with the rail section impactor are shown 

in Figure 105. The impactor forms a dent in the head shield and head at the impact location and 

the rail punctures the head. The section of the 11-gauge jacket supporting the head shield buckles 

as a result of the offset impact loads. The corresponding puncture behavior in the detailed impact 

patch for the rail section impactor is shown in Figure 106. As a result of the offset impact the

damage is greatest at the stress concentrations at the corners of the rail head and the puncture 

initiates at these sites. The puncture then progresses to the point that a rail shaped flap of material 

is punched in the tank head. 

The calculated force-deflection behavior for the rail section impact analyses is compared to those 

of the 3x3 and 6x6 inch impactors in Figure 107. The comparison shows that the rail impact 

more closely corresponds to the behavior of a 6-inch impactor. We can evaluate the 

characteristic size of the rail impactor by comparing the calculated head impact puncture force to 

the other impactors, as shown in Figure 108. The rail puncture force is shown using both the 3.7- 

and 5.8-inch initial estimates for the rail impactor characteristic size (defined previously in 

Section 3.2.4). The comparison in Figure 108 indicates that the upper range 5.8-inch 

characteristic size estimate correlates best with the linear fit generated from the other simple 

impactor geometries. 

An additional head impact analyses was performed using the rail impactor in an upside-down 

orientation. In this impact scenario, the wider bottom flange of the rail is the primary contact 

zone against the head. The calculated puncture behavior in the impact zone for the upside-down 

rail impactor is shown in Figure 109. A comparison of the corresponding force-deflection curves 

for the rail impactor in the two orientations is shown in Figure 110. The comparison shows that 

the orientation does not have a big effect on the puncture force. The puncture energy is increased 

by approximately 20 percent for the upside-down orientation impact. 

 

(a) Impact configuration (b) Impact behavior

Figure 105. Analysis of the 11-mph rail section impact behavior on the constrained head.
88 

(a) Before puncture (b) Puncture mode

Figure 106. Calculated head impact puncture behavior for the rail section impactor.

Figure 107. Calculated head puncture impact response for the rail section impactor.
89 

Figure 108. Calculated head impact puncture forces for various impactors.

(a) Before puncture (b) Puncture mode

Figure 109. Calculated head puncture behavior for the upside-down rail impactor.
90 

Figure 110. Calculated head impact response for the rail section impactors.

Coupler Impactor

A significant impactor threat for the tank head is a coupler. To evaluate this threat, the coupler 

impactor model, shown previously in Figure 87, was used to calculate the head impact puncture 

behavior. The initial impact analysis was performed with the constrained tank head impact 

configuration and an impact speed of 18 mph. The calculated head deformations for the 18-mph 

coupler impact are shown in Figure 111. The coupler impact forms a dent in the head shield and 

head at the impact location. The section of the 11-gauge jacket supporting the head shield 

buckles as a result of the offset impact loads. 

(a) Impact configuration (b) Impact behavior

Figure 111. Analysis of the 18-mph coupler impact behavior on the constrained head.
91 

The corresponding damage on the inside surface of the tank head is shown in Figure 112. This 

damage profile shown in Figure 112 corresponds to the end of the analysis where the ram has 

rebounded and the contact force between the tank head and coupler are zero. The coupler impact 

was not sufficient to fully penetrate the tank head but the damage under the location of the

greatest load concentration formed an incipient through crack in the head that would result in a 

release. The crack develops at a time close to the maximum ram displacement of approximately 

31 inches. 

A second coupler head impact analysis was performed where the impact speed was increased 

from 18 to 25 mph. At this impact speed, the coupler has sufficient impact energy to fully 

penetrate the tank head for this scenario. The puncture response is shown in Figure 113. The 

damage is shown at two times corresponding to a 32-inch ram displacement where a through 

crack in the head is fully developed and after the coupler has fully penetrated the tank head and 

the impact loads have significantly dropped (approximately 46 inches of ram displacement). 

 

Figure 112. Calculated damage for the 18-mph coupler impact on the constrained head.

The calculated force-deflection behaviors for the two coupler impact analyses are compared to 

those of the 9x9 and 12x12 inch impactors in Figure 114. The force-deflection behaviors were 

very similar for the two coupler impact analyses up to the maximum displacement of the 18-mph 

impact. At the higher impact speed, the forces continue to rise until the coupler fully punctures 

and penetrates the tank head. The comparison to the idealized impactors in Figure 114 shows that 

the coupler impact more closely corresponds to the behavior of the 12-inch impactor. However, 

the point at which a through crack penetrates the tank head corresponds to a puncture energy of 

3.15 million ft-lbs which is between that of the 9-inch and 12-inch impactors. 

We can evaluate the characteristic size of the coupler impactor by comparing the calculated head 

impact puncture force to the other impactors, as shown in Figure 115. The coupler puncture force 

shown in Figure 115 is the force at which the through crack is formed in the tank head (at 

approximately 32 inches of ram displacement). The comparison in Figure 115 indicates that the 
92 

coupler impactor has a characteristic size of approximately 10.8 inches based on the linear fit 

generated from the other simple impactor geometries. 

 

(a) Initial head puncture (32-inches ram displacement)

 

(a) Full head penetration (46-inches ram displacement)

Figure 113. Calculated damage for the 25-mph coupler impact on the constrained head.
93 

Figure 114. Calculated head puncture impact response for the rigid coupler impactor.

Figure 115. Calculated head impact puncture forces for various impactors.

3.3.3 Analysis of Offset Head Impact Location Effects

The above analyses all used the baseline offset head impact configuration. A parameter of

interest is the impact location on the head. In this idealized impact scenario, the sill is not 

modeled so the distance from the tank head center should be similar in any direction. As a result, 

a set of analyses was performed using the half head model with one symmetry plane and 

different offset distances for the impact point. The offsets used are 0.0-inches (center impact), 

15.0-inches, 28.5-inches, and 40.0-inches. The head impact models for the offset impact 

scenarios are shown in Figure 116. 
94 

(a) Center impact (b) 15-inch offset

(c) 28.5-inch offset (d) 40-inch offset

Figure 116. Impact scenarios used in the vertical offset impact analyses.

A comparison of the calculated force-deflection curves for the four different offset head impacts 

are shown in Figure 117. As expected, the center head impact has the highest puncture force and 

puncture energy. At the center impact location, the behavior is nearly axisymmetric and the load 

around the perimeter of the impactor is more uniform, resulting in a higher puncture force. As 

the impact location moves further from the head, the angle between the normal vectors of tank 

head impact position and the impactor face becomes greater and the corresponding puncture 

force drops. 
95 

Figure 117. Calculated force-deflection behaviors for variable offset head impacts.

3.4 Analysis of Impact Speed Effects

For the analyses described in this report, the selection of the impact speed is primarily based on 

engineering judgment with the objective of picking an impact speed that will have a high 

probability of puncturing the tank but not have too large of a residual kinetic energy. The 

assumption is that the puncture energy for this impact speed is a good approximation to the 

threshold puncture energy for the tank. This methodology was used previously in the NGRTC 

program (Kirkpatrick, 2009a). In that study, some analyses were performed at different impact 

speeds to investigate the magnitude of the effects. In this section we revisit the impactor speed 

effects for the 600 lb chlorine tank car design and the updated impact analysis methodologies 

used in this study. 

3.4.1 Analysis of Impact Speed for Side Impacts

For this side impact comparison, a set of the normal side impacts summarized in Table 2 were 

repeated at higher impact velocities. The comparison of the original force-deflection curves for 

the 3-inch, 6-inch, 9-inch, and 12-inch square impactors and the corresponding behavior for the 

higher speed impacts is provided in Figure 118. In this comparison, the impact speed was 

increased by 5 mph for each of the impact scenarios. For many impacts the effects of the impact 

are relatively small with slightly higher forces produced by increased inertial resistance and 

corresponding small reductions in the ram displacement required to puncture the tank. 

For the larger impactors, the impact speed has a slightly larger effect on the impact behavior. For 

the 9-inch and 12-inch impactors the higher speed impact results in a puncture near the end stage 

of the initial loading response of the force-deflection curve. By increasing the impact speed, 

some of the late time tank impact kinematics and interaction with the reaction wall are 

eliminated (some of these boundary condition effects are discussed below as well as in Section 

4.3.1 of this report). As a result, the calculated puncture energy will be reduced at the higher 

impact velocity. 
96 

Figure 118. Comparison of side impact behaviors at different impact speeds.

The comparison of the puncture forces and puncture energies for the baseline and higher speed 

impacts are provided in Figure 119 and Figure 120, respectively. Overall, there is little difference 

in the puncture forces with a 4 percent reduction in the slope of the linear fit to the higher speed 

impacts. The effect of the impact speed on the puncture energies is slightly larger than on the 

puncture forces but still relatively small with on average an approximately 9 percent reduction in 

the puncture energies for the cases analyzed. 

Figure 119. Comparison of side impact puncture forces at different impact speeds.
97 

Figure 120. Comparison of side impact puncture energies at different impact speeds.

An alternative evaluation of the speed effects was performed by running the 9.55-inch-diameter 

impactor at impact speeds of 10, 15, 20, and 25 mph. A comparison of the force-deflection 

behaviors is shown in Figure 121. All the curves have similar behaviors in the initial phase of the 

impact loading. However, the effects of the unloading and interaction with the wall appear much 

earlier in the force-deflection behavior for the lower speed impacts. Note that the 20 and 25 mph 

impacts puncture the tank, but the 15 and 10 mph impacts are below the puncture threshold for 

this tank and impactor. 

Figure 121. Comparison of the tank side loading response at different speeds.

An alternative comparison for the different speed impacts, shown in Figure 121, is to plot the 

force-time histories, as shown in Figure 122. In this comparison we see that the timing for the 

initial unloading is similar and initiates at around 150 ms. However, the point at which the wall 
98 

interaction and reloading of the tank occurs is earlier for the higher speed impacts. This is a 

result of both the ram and tank moving at a higher speed in the unloading for the higher speed 

impact scenarios. 

Figure 122. Comparison of the tank side loading response at different speeds.

The lower bound of side impact speeds was analyzed for the 9.55-inch-diameter round impactor. 

An analysis was performed using a steady rate displacement control boundary condition at a 

loading rate sufficiently slow to minimize dynamic impact effects (quasistatic). The calculated 

force-deflection behavior for this analysis is compared to the 25-mph impact in Figure 123. 

Figure 123. Comparison of the tank side loading response at different speeds.
99 

The comparison shows that the puncture forces again are similar, but the loading rate can 

significantly change the force-deflection behavior for this side loading scenario. These effects, 

and their interaction with different tank BCs, will be explored further in Section 4. 

3.4.2 Analysis of Impact Speed for Head Impacts

A set of analyses were performed to evaluate the effects of the impact speed for the baseline 

constrained tank head impact condition. The head was pressurized to 100 psi and the 6x6 inch 

square impactor was used. Impact analyses were performed at 11 and 14 mph. In addition, a 

quasistatic loading was applied where the ram was given a steady rate displacement control 

boundary condition at a rate sufficiently slow to minimize dynamic impact effects. 

The calculated head force-deflection characteristics for the three loading rates are compared in 

Figure 124. The comparison shows that there is little difference in the calculated deformation or 

puncture behavior. Thus, the behavior of the constrained tank head is mostly independent of the 

impact speed. The corresponding effects for a head impact on an unconstrained tank will be 

explored further in Section 4. 

Figure 124. Comparison of Head impact behaviors at different impact speeds.

3.5 Analysis of Tank and Lading Temperature Effects

An important assumption used in the above impact analyses are that the tank and lading are at a 

nominal temperature of approximately 78o

 F. From the chart of chlorine physical properties in 

Figure 125, this temperature produces an internal vapor pressure for the tank of 100 psi. The 

corresponding outage volume for a tank loaded to the specified limit would be 10.6 percent. In 

this section, we investigate the effects that the lading will have on the impact and puncture 

response if the temperature is significantly different. 
100 

Figure 125. Physical properties of chlorine as a function of temperature.

From the physical properties shown in Figure 125, we see that the vapor pressure increases, and 

the liquid density decreases as the temperature rises. A decrease in the liquid density will 

produce an increase in the liquid volume with a corresponding reduction in the outage volume. 

Both increasing the pressure and reducing the outage can reduce the puncture resistance of a tank 

car. As a result, a higher temperature for the tank and lading are expected to lower the tank 

puncture energies in impacts. 

The condition analyzed in this section is a 105J600W chlorine tank car at an equilibrium 

temperature of 105o

 F. This temperature increases the internal vapor pressure for the tank to 155 

psi and lowers the corresponding outage volume for a tank loaded to the specified limit to 7.5

percent. The resulting pressure-volume relationships for the chlorine tank at 78o and 105o F are 

compared in Figure 126. The comparison shows that the higher temperature results in 

significantly higher pressures at the initial condition and the pressures rise more rapidly as a 

result of volume changes produced by dent formations. 

The calculated puncture forces and energies in normal side impacts for the chlorine tank car at 

the two temperature conditions are compared in Figure 127 and Figure 128. The comparison 

shows that the temperature has little effect on the puncture forces. This result was expected since 

the puncture force for a given impact geometry is primarily a function of tank shell thickness and 

strength which are unchanged in these scenarios. However, the corresponding puncture energies 

are reduced on average approximately 25 percent. 

In addition to the normal side impacts, a set of 45-degree oblique impacts were also performed 

for the 105J600W chlorine tank car at an equilibrium temperature of 105o F. A summary of 

results for all the normal and oblique impacts for the tank at higher temperature is given in 

Figure 129. In the figure, the calculated puncture energies at 105 F are normalized by the 

puncture energies at 78o F for the corresponding impact conditions. In addition, an average value 

line is added to the graph. We see that on average, the increase in temperature dropped the 

puncture energies by 20 percent. However, the puncture energies for smaller impactor sizes are 
101 

more similar at the two temperatures. This is because the impact response for small impactors is 

dominated more by the structural stiffness. The internal pressure (and pressure increase) plays a 

smaller roll for the small dent sizes prior to puncture with the small impactor sizes. 

Figure 126. Pressure-volume relationships for the chlorine tank car at 78o and 105o F.

Figure 127. Comparison of side impact puncture forces at 78o and 105o F.
102 

Figure 128. Comparison of the side impact puncture energies at 78o and 105o F.

Figure 129. Normalized side impact puncture energies at 105o F.
103

4. Analysis of General Impact Conditions

4.1 Introduction

In this section, the detailed BW failure model described in Section 2 is applied to assess various 

tank and head puncture conditions. The analyses in this section are focused on expanding the 

impact scenarios to understand the tank response when exposed to more general impact 

conditions. 

4.2 Oblique Impacts

An initial set of oblique impact analyses was performed using the 12x12 inch square impactor at 

an impact speed of 25 mph. The obliquity angles were 15, 30, and 45 degrees as shown in Figure 

130. These oblique impact analyses are significantly different than the rotated impactor analyses, 

previously described in Section 3.2.4, because the impactor trajectory is now rotated relative to 

the tank axis. In the rotated impactor analyses the orientation of the impactor was rotated but the 

impact trajectory was still normal to the tank. The force deflection curves for these oblique 

impacts are compared to each other and to the normal impact in Figure 131. 

(a) 15-degree obliquity (b) 30-degree obliquity (c) 45-degree obliquity

Figure 130. Various oblique impact conditions investigated for side impacts.

The force deflection characteristics for the oblique impacts show a few specific trends. First, the 

force level at which the tank punctures is reduced for higher obliquity angles. This trend is 

expected since the impact face is now rotated relative to the tank wall producing stress 

concentrations at the edges and corners of the impact face (as seen in the rotated impactor 

analyses described in Section 3.2.4). 
104

Figure 131. The effects of impact obliquity on the tank impact and puncture response.

One significant difference seen in the oblique impacts compared to the normal impact with a 

rotated impactor is the puncture initiation behavior. A sequence of the impact damage and failure 

of the tank wall for the 45-degree oblique impact is shown in Figure 132. The sliding contact 

with the oblique impact results in large concentrations of damage at the corners of the impactor. 

These concentrations result in cracks that penetrate the tank wall significantly earlier than the 

time at which the entire impact face punctures the tank wall. Thus, with this type of oblique 

impact scenario, it is possible to have conditions that produce small cracks through the tank wall 

but do not produce a large puncture hole. 

A second unique feature of the force-deflection curves in Figure 131 is that the slope of the 

force-displacement curve is reduced as the impact obliquity increases. However, this can be 

attributed to the reference displacement in the plot being the ram displacement which is no 

longer normal to the tank axis. If we modify the plot to use only the component of displacements 

normal to the tank axis, the slopes of the curves are much more consistent, as seen in Figure 133. 

This suggests that the force buildup is a function of the component of the ram displacement 

normal to the tank axis. 
105

(a) Initial impact

(b) Fracture at impactor corners

(c) Full tank puncture

Figure 132. Oblique impact damage development and puncture behavior for side impacts.
106

Figure 133. The effects of impact obliquity on the tank impact response and puncture.

Further insight into the oblique impact behavior can be obtained by comparing the oblique 

impact with the normal impact where the impactor face is rotated by the same angle. Here we 

will compare the 45-degree rotated impactor and 45-degree oblique impact configurations shown 

in Figure 134. The comparison of the corresponding force-displacement curves for these two 

impact scenarios is shown in Figure 135 (using the tank normal displacement). By correcting for 

the tank normal displacement, the two curves have a similar slope. In addition, by using the 

rotated impactor, the puncture forces and puncture energies are relatively similar. 

In addition to the above oblique analyses with the 12x12 inch square impactor, a full set of 

analyses was performed with the full range of impactor sizes and shapes at a 15, 30, and 45-

degree oblique impact angle. Comparisons of the normal and oblique impact puncture forces and 

energies are provided in Figure 136 and Figure 137, respectively. The puncture forces are 

reduced with increasing obliquity angles and at the 45-degree oblique impacts the puncture 

forces are more than 50 percent lower than the normal impacts for the largest impactor. 

However, as the impactor size is reduced the differences in puncture force are also reduced. At a 

6-inch characteristic size the 45-degree oblique impact puncture force is only reduced by 40

percent compared the normal impact. Finally, for the 3x3 inch impactor there is very little 

difference between the normal and oblique impact puncture forces. As a result, a linear fit to the 

oblique puncture force data would not intercept the origin of the graph as used in the normal 

impact data. The fits shown for the oblique impacts correlate the puncture forces to the square 

root of the impactor characteristic size. 
107

(a) 45-degree impactor Rotation (b) 45-degree oblique impact

Figure 134. Effect of impactor angle on oblique impact response for side impacts.

Figure 135. The effects of impact obliquity on the tank impact response and puncture.
108

Figure 136. Comparison of puncture forces for normal and oblique impacts.

Figure 137. Comparison of puncture energies for normal and oblique impacts.

The puncture energies for the oblique impact show similar trends to the puncture forces. The 

puncture energies for the largest impactors are reduced by roughly 70 percent. Again, as the 

impactor size is reduced the differences in puncture energies are also reduced. At a 6-inch 

characteristic size the oblique impact puncture energy is only reduced by 50 percent compared 

the normal impact. Finally, for the 3x3 inch impactor there is very little difference between the 

normal and oblique impact puncture energies. For the oblique impact puncture energies, a linear 

fit of the data was used. 
109

4.3 Impact Boundary Condition Effects

4.3.1 Side Impact Constraint Effects 

A series of analyses were performed to investigate the effects of the constraint level on the tank 

response. The initial analyses are for the side impact of the 600 lb chlorine tank car. The 

impactor selected for these analyses was the 9.55-inch-diameter round impactor. Three different 

levels of constraint were considered as shown in Figure 138. The highly constrained boundary 

condition is the tank shown in Figure 138(a) backed by the rigid impact wall that has been used 

for the majority of the side impact analyses in this report, as well as the previous NGRTC 

analyses (Kirkpatrick, 2009a). The unconstrained boundary condition is a single tank that is free 

to translate, shown in Figure 138(b). The moderately constrained boundary condition is two 

deformable tanks sitting side-by-side, shown in Figure 138(c). 

(a) Highly constrained tank (reaction wall) (b) Unconstrained tank (free)

(c) Moderately constrained tank (side-by-side tanks)

Figure 138. Various tank motion constraint BCs for side impacts.

One of the issues in evaluating the effects of the BCs is that for many impact conditions the 

constraint on the back of the tank is not significant. If the impact speed is sufficiently high for a 

given size impactor, the tank will be punctured before there is sufficient time for the tank to 

move. For example, the force-deflection curves for the 25-mph impact of the 9.55-in-diameter 

impactor for the 600 lb chlorine tank car with the impact wall and free BCs are compared with 

the red and blue curves in Figure 139. The comparison shows that the curves are nearly identical 

and the constraint conditions behind the tank are not significant for this impact scenario. With a 

fully loaded tank and relatively fast impact speed, the inertial constraint of the tank is the 

dominant factor. This example demonstrates that the scenario selected for the assessment of the 
110

BCs is important. It must have a sufficiently large impactor moving sufficiently slowly to allow 

for the constraint conditions behind the tank to be significant. 

To further demonstrate the importance of the inertial constraint on this impact scenario, the two 

25 mph impacts using the 9.55-in-diameter impactor (wall and free) were repeated but the target 

tank models were modified to have the weight of an “empty” tank (the lading pressure effects 

were maintained). The comparison of the behaviors for the baseline and lighter “empty” tanks is 

shown with the black and green curves in Figure 139. The comparison shows that the lighter 

tanks develop forces more slowly since the ram motion does not need to accelerate as much 

mass. Similarly, the effects of the tank dynamic response and BCs are seen much earlier since 

the lighter tank has higher natural response frequencies. For these analyses the boundary 

constraint plays a large role. The tank constrained by the impact wall provides a reaction force 

where the impactor loads recover and eventually puncture the tank. The free tank is pushed 

away from the impactor and is not punctured.

To investigate the boundary constraint effects, a modification was made to the impactor BCs. In 

the majority of analyses performed in this study, the impactor was designed to represent the ram 

car from the NGRTC program (Kirkpatrick, 2009a). As such, the impactor model was given a 

295,000 lb weight with an initial impact velocity and was constrained to 1D motion along the 

initial trajectory. The impactor was free to decelerate and even reverse direction as it interacted 

with the target tank. 

Figure 139. The effects of constraint conditions for a 25-mph impact and 9.55-inchdiameter impactor, with differing tank weights.

For many of the analyses in this section, the impactor was prescribed to have a constant velocity 

impact condition. This is more representative of the loading for an impactor that is attached to a 

longer section of train in a derailment where the very large mass results in small changes in 

impactor velocity over the duration of any individual impact event. A comparison of the forcedeflection characteristics for the side impact response with the three different constraint 

conditions (wall, tank, free) is shown in Figure 140. For reference, a corresponding force-
111

deflection curve for the impact scenario of a 25-mph impact with the 295,000 lb impactor is also 

shown on the graph. 

The comparison shows that the initial portion of the force-deflection curves for all three 15 mph 

impacts are identical (up to approximately 30 inches ram displacement). All three impacts reach 

an initial peak force that was very close to the failure level before the dynamic response of the 

tank results in a temporary drop in the impact force (at approximately 40 inches displacement). 

Beyond this time, the tank constraint BCs begin to play a large role in the behavior. With the 

highly constrained impact wall scenario the impact force quickly recovers, and the tank is 

punctured at approximately 48 inches of ram displacement. With the moderately constrained 

side-by-side tank scenario the impact force more slowly recovers, and the tank is punctured at 

approximately 56 inches of ram displacement. Finally, with the unrestrained tank the impact 

force never fully recovers to the puncture force level and the tank does not puncture. 

Figure 140. The effects of constraint conditions for the 15 mph constant velocity impacts.

To further remove the effects of the tank dynamics from the impact behavior, an additional 

analysis was performed using a constant velocity of the ram of approximately 0.5 mph. This 

slow impact speed eliminates most of the tank dynamic effects and approximates a quasistatic 

loading of the tank between the ram and the wall. The force deflection for this quasistatic 

analysis is compared to those of the 25-mph initial velocity and 15 mph constant velocity 

impacts in Figure 141. Without the dynamic effects, the initial portion of the force-deflection 

curve is lower for the quasistatic analysis. However, as the tank is compressed and the internal 

pressure increases, the slope of the force-deflection curve rises and the tank punctures at 

approximately 40-inches of displacement. The internal pressure rises from 100 psi initially to 

over 130 psi at the point of puncture for this analysis. 

The wall provides a relatively high level of constraint against the tank translation in side impacts. 

However, it still allows for motion of the tank center of gravity (CG) away from the direction of 

impact. An idealized impact scenario that does not allow for any translation of the tank CG is to 

add the third symmetry plane to the tank normal to the direction of the impact. This is equivalent 

to a tank being impacted symmetrically between impactors on either side of the tank. An 
112

example of the model and impact response for this symmetric impact condition is shown in 

Figure 142. 

Figure 141. The effects of impact speed on the highly constrained side impacts.

Two analyses were performed for the symmetric impact condition with the 105J600 chlorine 

tank car. Both analyses used the 9.55-in-diameter impactor. The difference is that the first 

analysis used a constant velocity 15 mph impact speed, and the second analysis was performed at 

a much slower quasistatic loading condition. The calculated force deflection behaviors for these 

two analyses are shown in Figure 143. For comparison, the force deflection curve for the 

quasistatic loading of the tank against the wall is included in the figure. 

The comparison of the behaviors using the symmetric BC helps to develop an improved 

understanding of the tank response. The first observation is that the gross behaviors of the 

quasistatic and 15 mph analyses are similar, and both fail at nearly identical displacements and 

forces. The primary difference is that the 15-mph impact behavior has some effects of the tank 

dynamic vibrations superimposed on the quasistatic force deflection path. 

The other interesting comparison is between the quasistatic loading for the symmetric BC and 

the quasistatic loading against the wall. Both cases have relatively linear force deflection curves, 

and both fail at roughly equivalent puncture forces. However, the symmetric loading fails at a 

ram displacement of approximately 30 inches and the loading against the wall fails at a ram 

displacement of approximately 40 inches. However, the symmetric condition assumes that the 

tank is between two moving rams. Thus, the total compaction of the tank between the two ram 

faces is approximately 60 inches. 
113

(a) Initial condition (b) Early impact

(c) Before tank puncture (d) After tank puncture

Figure 142. Calculated response for the symmetric tank side impact scenario.

The comparison can be further used to estimate the stiffness of the tank compressed against the 

wall. If we use the symmetric analyses to determine that the dent depth around the impactor is 30 

inches at the time of puncture, then the compression of the far side of the tank against the wall 

has a 10-inch depth. We would expect this depth to be much smaller than the ram dent depth 

since the loaded area is very large, but the total wall reaction force is equal to that on the ram 

face. To investigate the wall reaction stiffness, an additional analysis was performed where the 

tank was quasistatically compressed between two reaction walls (symmetric analysis with a 

moving wall). The calculated force-deflection for the symmetric wall loading is compared to the 

to the other quasistatic load cases in Figure 144. The comparison shows that the 1.5 million lb 

reaction load develops over a displacement of approximately 10 inches (after the initial 4-inch 

standoff distance of the jacket from the tank is crushed). 
114

Figure 143. The effects of constraint BCs on the side impact response.

Figure 144. The effects of constraint BCs on the side impact response.

1.1.1 Head Impact Constraint Effects 

A similar set of analyses were performed to investigate the effects of the constraint BCs on the 

head impact response. The baseline head impact conditions, adapted from the NGRTC program, 

were for a highly constrained tank head mounted on a test frame that does not allow for any 

motion at the specimen support. The head impact specimen included the tank head and head 

shield, supported by a short length of the tank shell and jacket, which were welded to a rigid test 

frame. A model for these highly constrained head impact conditions is shown in Figure 145(a). 

In the model, the nodes at the back of the shell and jacket section are fixed and do not allow for 

any displacement or rotations. 
115

(a) Highly constrained head motion (fixed BC)

(b) Unconstrained tank motion (head impact)

Figure 145. Various tank motion constraint BCs for side impacts.

To investigate the constraint effects in head impacts an unconstrained tank model was developed 

as shown in Figure 145(b). The model includes the entire tank which is free to translate. Gravity 

was included in the analyses to develop appropriate vertical forces and motions in the offset 

impact scenario. Without the test frame support, a model of the ground was needed to resist the 

gravitational free-fall motions of the tank. The tank is free to slide along the ground as a result of 

the impact. 

One factor of the head impact response that was unknown is how the lading couples to the tank 

motions. To determine the bounds on the effect an initial pair of analyses was performed where, 

in the first analyses, none of the weight of the lading was added to the tank, and in the second 

analysis, all the lading mass was smeared into the tank. The force deflection curves for these two 

analyses are compared to that of the fully constrained tank head impact analysis in Figure 146. 

The analyses are for an 18-mph impact of the 9.55-inch-diameter round impactor at 18 mph. 
116

Figure 146. The effects of BC restraint on head impact response 

(18 mph impacts).

The force-deflection curve for the highly constrained tank head has a roughly linear relationship 

between the ram displacement and impactor force up to a puncture force of approximately 1.8 

million lbs at a ram displacement of approximately 25 inches. The force-displacement curves for 

the two unconstrained tank models start along the same force deflection curve. However, the 

force curves for both begin to fall below that of the constrained head force curve. The rate at 

which to force curve diverges is much more rapid for the light tank than the heavy tank. This is 

because the impact forces can push the light tank away from the impactor more rapidly than the 

heavy tank. 

A similar set of analyses was performed on the tank and tank head using the coupler impactor 

model and an impact speed of 25 mph. The analyses again included the bounds of the empty and 

fully laded tank weights. The force deflection curves for these two analyses are compared to that 

of the fully constrained tank head impact analysis in Figure 147. The trends are very similar to 

those of the 18-mph impact. These results will be discussed further in the development of a 

simplified head impact analysis algorithm, described in Section 6.2 of this report. 
117

Figure 147. The effects of BC restraint on head impact response 

(25 mph coupler impacts).

4.4 Lading Response Effects

4.4.1 Lading Effects for Side Impacts

A set of preliminary analyses were used to assess the effects of the lading in the side impact 

response during the NGRTC program (Kirkpatrick, 2009a). The impact conditions for this 

analysis were the Test 1 side impact conditions from the NGRTC project on April 26, 2007, at 

the Transportation Technology Center, Inc. (TTCI) in Pueblo, Colorado (Witte & 

Anankitpaiboon, 2007). This test involved a side impact of a 23x17 inch impactor with 1-inchradius edges and corners into the side of a 105J500 chlorine tank car backed by a rigid impact 

wall. The ram car impact speed was measured optically at 13.9 mph using speed trap reflectors 

placed within 6 feet of the impact point.

Additional parameters for Test 1 were as follows:

• Tank Car Weight (estimated) 265,000 pounds

• Tank Shell: 0.777-inch-thick normalized TC128B

• Jacket: 11-gauge A1011 steel at 4-inch standoff distance

• Slurry Density 11.6 lb/gallon

• Outage 10.4 percent

• Capacity 17,391 gallons

• Internal Pressure 100 psi

• Ram Car Weight: 285,600 pounds

• Ram Car Energy (derived): 1.86 million foot-pounds 
118

A tank car model was developed and used to predict the Test 1 impact response. The model of 

the 105J500 chlorine tank car is shown in Figure 148. The model includes the commodity tank, 

jacket and jacket standoffs, sill and bolsters, trucks, and outriggers attached to the draft gear to 

prevent a post-test rollover of the target tank caused by the rebound off the reaction wall. 

There are many different modeling approaches that can be used to include the dynamic effects of 

the fluid lading. The different modeling methodologies have tradeoffs on accuracy, efficiency, 

and utility. Some of these methodologies have been investigated in studies for side impacts of 

tank cars [e.g., (Kirkpatrick, 2009a), (Jeong, et al., 2009), (Tang Y. H., et al., 2007), (Tang Y. H., 

Yu, Gordon, Jeong, & Perlman, 2008)]. An example is the simplified explicit model of the lading 

included in the tank car model in the NGRTC program, shown in Figure 149 (Kirkpatrick, 

2009a). The lading model consisted of a low strength viscoelastic material that fills the same 

volume as the slurry added to the test tank. The sloshing of the lading model can be seen in the 

cutaway view of the predicted impact response. This lading modeling approach was established 

to capture some of the momentum transfer of the coupled fluid-structure response but to 

minimize effects such as sloshing at the fluid free surface that can cause numerical stability 

problems. 

(a) Complete tank car model

(b) Tank car mesh

Figure 148. Updated model generated for a 105J500W pressure tank car.

 (a) Before impact (t=0.1 s) (b) Near max. displacement (t=0.25 s)

Figure 149. Calculated Test 1 impact response with cutaway showing lading.
119

The comparison of the predicted and measured force-deflection curves is shown in Figure 150. 

The comparison of the force-deflection behaviors shows good agreement between the calculation 

and the test. The comparison of the pretest prediction and impact test serves as a validation of the 

model for the tank collision dynamics and impact deformation behavior. The responses include 

the initial impact, the reaction of the impact loads against the wall, and the post-impact rebound 

from the wall. Additional details of the impact behavior captured in the model included the target 

tank roll motion and lifting forces on the ram car caused by the lateral support of the target tank 

truck on the stub rail sections and the action of the outriggers resisting a post-test rollover 

behavior. 

In this study, an additional series of calculations was performed for this impact condition to 

evaluate the effects of various approximations to the lading models and BCs used in the analyses 

of side impacts. The three different BCs analyzed are shown in Figure 151. The first boundary 

condition, shown in Figure 151(a), is the idealized case where the tank is assumed to have 

vertical symmetry and no vertical gravitational loads are imposed. This is the simplest 

approximation and was used for the majority of analyses in this study. However, with symmetry 

and without gravity, this model is not suitable for explicit modeling of the effects of the lading 

sloshing behavior. The second boundary condition, shown in Figure 151(b), adds the effects of 

vertical gravitational loads and a rigid flat model of the ground to resist the vertical tank motions. 

The third boundary condition, shown in Figure 151(c), adds the effects of vertical gravitational 

loads and models of the bolsters and trucks to support the tank and resist vertical tank motions. 

As a simplification of this condition the motions of the wheels were fixed. 

Figure 150. Comparison of the measured and predicted Test 1 force-deflection curves.
120

 (a) Tank model with vertical symmetry (b) Tank supported on ground

(c) Tank supported on trucks

Figure 151. Various model support BCs for a 105J500W pressure tank car.

The calculated tank impact force histories with the smeared lading model and the three different 

support BCs are compared to the measured impact force history in Figure 152. The response for 

the models with the vertical symmetry and the tank supported on the ground are very similar to 

each other and agree well with the peak force levels for both the initial loading and secondary 

loading to the maximum force for this test. The model supported on the trucks also agrees well 

with the initial loading and first force peak. However, the model with trucks unloads more 

slowly and does not accurately capture the reloading to the secondary peak force level. The 

reason for this discrepancy was not determined. However, it is possible that approximations such 

as the constrained motions of the wheels and the constrained vertical motion of the impactor 

resist the rotational movement of the tank for this scenario and modify the impact dynamics. 

A second analysis was performed on the model with the truck support BCs to reassess the effects 

of the modeling approximations for the lading. In the analysis, an alternative mesh-free 

Smoothed Particle Hydrodynamics (SPH) approach is used to model the lading. This has the 

advantage of being able to capture the fluid sloshing without mesh distortion effects and possible 

numerical instability of classical Lagrangian analyses. The SPH methodology is also compatible 

with the traditional Lagrangian analysis methodologies being used to evaluate the tank response. 

As a result, it is more computationally efficient than the Arbitrary Lagrangian Eulerian (ALE) 

methodologies that have been used for the fluid-structure interaction in tank car impacts cars [

(Jeong, et al., 2009), (Tang Y. H., et al., 2007), (Tang Y. H., Yu, Gordon, Jeong, & Perlman, 

2008)]. 
121

Figure 152. Calculated tank car impact behavior using three different support BCs.

The calculated Test 1 side impact tank and lading deformations at various times during the 

impact are shown in Figure 153. The corresponding force-time histories for the analyses with the 

smeared and SPH lading models are compared to the measured behavior in Figure 154. With the 

SPH lading model, the initial unloading occurs earlier and the reloading to a second peak force is 

more accurately reproduced. The timing of the initial and secondary force peaks is in good 

agreement with the experiment. The primary differences from the measured behavior are that the 

drop in load after the initial force peak is not as rapid or as large as measured, and some of the 

higher frequency response characteristics are dampened by the SPH lading model. 

The above analyses of the Test 1 impact conditions with different lading models and tank BCs 

illustrate the complexities of this test configuration. The late time response will be influenced to 

varying degrees by the constraints on the lateral, vertical, and rotational motions as well as the 

modeling of the lading. However, all the modeling approximations agree well with the initial 

loading response which is the most important portion of the impact response (punctures often 

occur during this initial loading). In addition, the various modeling methodologies all give 

reasonable estimates for the duration and amplitude of the impact force pulse. 
122

(a) Before impact (time=0.0 s) (b) Near first load peak (time=0.10 s)

(c) Near second load peak (time=0.25 s) (d) After unloading (time=0.50 s)

Figure 153. Calculated side impact response with SPH lading model.
123

Figure 154. Calculated tank car impact behavior using two different lading models.

4.4.2 Lading Effects for Head Impacts

A similar head impact analysis in an unconstrained tank was performed using an 18-mph impact 

with the 9.55-inch-diameter impactor. Again, the impact was analyzed with the SPH lading 

model. The calculated tank and lading deformations at various times during the impact are 

shown in Figure 155. The corresponding force-displacement curve is compared with the 

analyses with the similar impact condition for the empty and loaded weight models in Figure 

156. The comparison shows that the force-deflection curve for the SPH model is closer to that of 

the empty tank weight than the smeared mass model of the fully loaded tank. This suggests that 

only a fraction of the lading mass couples to the motions of the unconstrained tank in head 

impacts. This effect is confirmed by including fringes of longitudinal velocity in the lading as 

shown in Figure 157. The time shown is well past peak load halfway through unloading. 

However, the bulk of the lading is still stationary (blue fringes in the figure). Only the regions of 

the fluid very near to the tank wall or directly behind the impacted tank head are moving. 
124

(a) Before impact (time=0.1 s)

(b) Near load peak (time=0.16 s)

(c) After unloading (time=0.22 s)

Figure 155. Calculated head impact response with SPH lading model.

Figure 156. Calculated tank car head impact behavior using different lading models.
125

(a) Full tank profile (time=0.18 s)

(b) Impact zone (time=0.18 s)

Figure 157. Calculated longitudinal velocity distribution in the SPH lading.

To investigate the effective weight of the fluid lading contributing to the motion in the head 

impact, we applied the impact response algorithm, described in Section 6.2.1, to run analyses at 

different tank weights and iterate on an approximate equivalent weight of the tank. The value 

that matched the analysis best was a tank weight of 130 percent of the empty weight. To confirm 

this result, we performed an additional finite element impact scenario where the weight of the 

tank was equal to 130 percent of the empty weight using a smeared mass approach (increasing 

the density of the commodity tank material). The comparison of this analysis with the 130

percent tank weight with the empty tank model, the full weight model (smeared mass) and full 

model with SPH lading is shown in Figure 158. The agreement of the SPH model with the 130

percent tank weight model is quite good. Note that the 130 percent weight model increases the 

tank from an empty weight of 61,300 lbs to a weight of 79,690 lbs. The full weight of the tank is 

263,000 lbs which is the empty tank plus approximately 200,000 lbs for the lading. As a result, 

these analyses show that less than 10 percent of the lading is coupled to the motion of the tank 

for this head impact scenario. 
126

Figure 158. Calculated tank car head impact behavior using different lading models.

4.5 Head Impact Test Configuration

One of the important tank head protection requirements is to provide for the puncture resistance 

of a coupler impact at a relative impact speed of 18 mph. This head impact condition is designed 

to verify the integrity of new or untried tank head puncture protection systems and to test for 

system survivability after coupler-to-tank-head impacts. We have already analyzed many aspects 

of this head impact scenario including the effects of a coupler impacting the constrained tank 

head in Section 3.3.2, the effects of the BC constraints in Section 1.1.1, and the effects of the BC 

constraints in Section 4.3.2. In this section we extend these analyses to further analyze the head 

impact test configuration. The details of the head impact testing requirements are provided in 

Appendix A of this report. 

The head impact condition uses a rigid 263,000-pound ram car equipped with a coupler, and a 

draft sill including the draft yoke and draft gear. The coupler protrudes from the end of the ram 

car so that it is the leading location of perpendicular contact with the impacted test car. The 

impacted test car is loaded and pressurized to 100 psi. In addition, the target tank car is coupled 

to a 200,000-pound rigid backup car (trailing mass) for a combined target total weight of 

486,000 pounds. The overall model configuration for a head impact analysis is shown in Figure 

159. The analysis was conducted with the coupler impacting on the lateral centerline of the tank 

car at a height of 21 inches above the top of the sill. 

Trailing Mass Tank Impactor

Figure 159. Tank head impact analysis model geometry.
127

1.1.2 Draft Gear Effects for the Impactor

There are several features of this head impact test configuration that add complexity. The first is 

the complex geometry of the impactor face with a coupler head impactor. This has already been 

analyzed for both side and head impacts and is discussed in Sections 3.2.4 and 3.3.2. The 

regulations of the testing configuration (49 CFR § 179.16) do not specify the specific coupler 

type or manufacturer. As a result, variations may exist in the impact face geometry that could 

influence the puncture potential. 

A second effect that complicates this test configuration is the use of the coupler impactor “sled” 

with a sill and draft gear. To investigate this effect, a model of a coupler impact sled was 

developed and used in an impact analysis. The model for the coupler impactor sled is shown in 

Figure 160. It consists of a large rigid sled with a mass of 263,000 lbs. This value was selected to 

conform to the regulatory coupler head impact test specification. A rigid sill was attached to the 

mass and a model of the coupler and draft gear was included in the sill. The model of the draft 

gear is shown in Figure 160(b). It includes an energy absorbing draft gear model, a realistic 

geometry of a draft gear yoke, and a draft gear design that applies a retaining key to holds the 

assembly together. Identical draft gear models were used in both the tank car and the rigid 

impactor block. The energy absorbing draft block allows for 3.2 inches of travel before the draft 

gear follower plate seats against the friction draft gear case and the gear creates a direct load path 

from the coupler to the lugs. 

(a) Full coupler impact sled model

(b) Coupler and draft gear model

Figure 160. Model of the 263,000 lb coupler impactor sled.

The force-deflection characteristics of the draft gear were obtained using a nonlinear spring with 

the specified properties shown in Figure 161. The draft gear develops a force of approximately 

500,000 lbs after one half inch of displacement that steadily increases to approximately 900,000 

lbs at approximately 3 inches of displacement. After the three inches of travel the loads increase 

rapidly. During unloading the force deflection behavior follows the same curve and there is no 

hysteresis to dissipate energy in the draft gear. This is a conservative assumption in that the draft 

gear loads will remain at elevated levels and more of the energy dissipation will occur in the tank 

head deformations. 

A comparison of the 25 mph impact behaviors of the restrained tank head using the initial rigid 

coupler impactor model and the new coupler impact sled model are shown in Figure 162. The 
128

higher 25-mph impact speed was used in these analyses to increase the impact severity to a 

condition that would puncture the tank head. Overall, the force deflection characteristics of the 

two impact analyses are similar. The slight reductions in impact force are probably a result of the

compaction of the draft gear allowing for a slight increase in the sled displacement compared to 

that of the coupler face. The larger discrepancy is in the point of failure initiation through the 

tank head. The impactor sled allows for small rotations of the coupler within the sill and this 

effect could allow for some redistribution of the contact loads across the coupler face. With the 

sled, the puncture force is increased by approximately 8 percent. However, with the additional 

compliance of the draft gear and the slope of the force-deflection curves, this results in a 27

percent increase in the puncture energy. 

Figure 161. Force-deflection characteristics used for the energy absorbing raft gear.

Figure 162. Comparison of 25 mph coupler impact and puncture behaviors.
129

4.5.1 Trailing Mass Effects for the Impactor

The head impact tests conditions specify that the impacted test car must be coupled to one or 

more “backup” cars to achieve a total weight of 217,724 kg (480,000 pounds) with hand brakes 

applied on the last “backup” car. To investigate the effects of the reaction forces from the backup 

car, a model for a 200,000 lb rigid trailing mass was generated and coupled to the test tank car. 

In the initial analyses, the tank was modeled at 130 percent of the empty tank weight using the 

smeared lading model approximation (1.3X). This provides the approximate inertial effects of 

the liquid lading in a head impact as shown in Section 4.3.2. 

The transfer of momentum in the impact analysis is shown in Figure 163. In the figure blue is 

stationery and red is the initial velocity of the impactor mass of 18 mph. The times shown are

before impact and at 40 ms intervals after impact. The corresponding velocity histories for the 

impact mass, the trailing mass, and the commodity tank are shown in Figure 164. The impact 

mass decelerates from the 18-mph initial velocity to less than 6 mph after impact. Similarly, the 

tank and trailing mass is accelerated to a velocity of greater than 10 mph after the impact. 

The corresponding impact forces for the tank and the transmitted forces to the trailing mass are 

shown in Figure 165. For comparison, an identical impact analysis was performed without the 

trailing mass coupled to the tank. The comparison shows that the trailing mass has only a modest 

influence on the peak impact force (approximately a 20 percent increase in the peak force). This 

modest increase in impact severity does not justify the significant increase in the complexity of 

the test conditions and collision dynamics. 

One of the modeling approximations used in this analysis of the head impact test condition is the 

1.3X lading model. As described in Section 4.3.2, this model couples less than 10 percent of the 

lading to the motion of the tank for this head impact scenario. This is probably appropriate for 

the early time motion of the tank including the peak impact force. However, at some later time 

the lading inertial effects will interact with the tank motions. To evaluate the bounds of the 

effects, an additional set of analyses was performed using the modeling approximation where all 

the lading mass was smeared into the tank model. 

The calculated velocity histories for the impact mass, the trailing mass, and the commodity tank 

for the smeared full lading model are shown in Figure 166. The impact mass decelerates from the 

18-mph initial velocity to approximately 4 mph after impact. Similarly, the tank and trailing 

mass is accelerated to an average velocity of approximately 8 mph after the impact. 

The corresponding impact forces for the tank and the transmitted forces to the trailing mass are 

compared to those of the 1.3X model in Figure 167. The comparison shows that the lading 

inertial approximation has a much larger effect than that of the trailing mass. In addition, with 

the smeared full lading model, the trailing mass has only a small influence on the peak impact 

force (approximately a 10 percent increase in the peak force). 
130

Figure 163. Momentum transfer for the tank car head impact analysis.

Figure 164. Velocity histories for the 1.3X lading head impact analysis.
131

Figure 165. Calculated impact behavior using the 1.3X lading model.

Figure 166. Velocity histories for the smeared full lading head impact analysis.
132

Figure 167. Calculated head impact behavior using the smeared full lading models.

4.5.2 Summary of the Head Impact Test Evaluation

The above analyses, supported by analyses in other sections of this report, allow for observations 

to be made about the head impact test requirement. The first observation is that the details of the 

test are not tightly controlled. This includes aspects of the coupler and draft gear geometry and 

energy absorbing characteristics, tolerances of the coupler and striker clearances that will allow 

for rotation of the coupler impactor face against the tank head, and the geometry of the impactor 

and trailing masses. Many features of the test could be changed that would increase or reduce the 

severity of the impact and the test conditions would still fall within the bounds of the testing 

specifications. 

An example of this test uncertainty is that the test requirements allow for one or more backup 

cars to be used to provide the inertial resistance to the impact. However, the analyses performed 

in this study illustrate that a single rigid mass coupled to the target tank car can provide only a 

modest level of inertial resistance to the initial impact forces. If this coupled mass was replaced 

by several lighter masses coupled together, each subsequent mass would contribute to a lesser 

extent and with a delayed effect. As a result, the inertial restraint of the backup cars could be 

minimized and still be within the allowable testing configuration. 

A second general observation is that the test is very complex both for the performance of an 

experiment and even more so for analysis of the test condition. To accurately model the test 

condition requires the modeling of the lading sloshing effects, the interaction of the target tank 

car and coupled “backup” cars, and the modeling of the impactor with a complex coupler 

impactor face and draft gear behavior. With all these effects, there are many potential modeling 

assumptions and approximations that could be applied by different analysts that would introduce 

large errors in the calculated impact forces and puncture resistance. 

Ideally, the head impact test condition should be replaced with one where the head is attached to 

a rigid mass with a well-defined attachment BC. The impactor should also effectively be a rigid 

mass with a well-defined impactor face geometry. The motions of the two bodies should be 
133

controlled to a one-dimensional translation. With these approximations the test will provide 

much more repeatable and reproducible results and the analyses will be greatly simplified 

reducing the potential errors from different modeling methodologies. 

4.6 Analysis of Offset Side Impact Effects

4.6.1 Analysis of Vertical Offset Side Impacts 

For the idealized side impact analyses, discussed in Section 3, the impact point was always at the 

center of the tank both along the length and at the vertical mid-height (belt line). In this section, 

we explore the effects of offsetting the impact position both vertically and longitudinally. 

The initial series of offset side impact analyses were performed on the side impact condition 

where the impact point was offset vertically by different magnitudes. This offset effect is similar 

to that of the analyses of the head impacts that have typically included the effects of an impact 

that was offset from the center of the tank head. The offset impact was found to influence the 

damage development of the tank head under the impactor and reduce the load at the puncture 

initiation. 

The vertical offset side impact analyses were performed using the 9.55-inch-diameter round 

impactor. In the idealized side impact analyses, described in Section 3.2, the models contained 

longitudinal and vertical symmetry planes to model one-quarter of the tank. That model reflected 

about the symmetry plane is shown in Figure 168(a). For the offset analyses, the vertical 

symmetry plane can no longer be used. As a result, BCs to control the vertical motions of the 

tank were needed. The methodology used was to apply gravity to the tank and to add a rigid 

ground model that supports the tank. The corresponding model for the center impact and impact 

points offset 15 and 25 inches below the centerline are shown in Figure 168(b-d). 

The calculated force-deflection histories for the four models shown in Figure 168 are compared 

in Figure 169. The idealized impact conditions with symmetry (Figure 168a) and the center 

impact analyses with ground and gravity added (Figure 168b) fail at roughly equivalent puncture 

forces and energies. There are slight differences introduced by the more complex BCs, but the 

overall behavior is similar, and the puncture energies are within 10 percent. However, as the 

impact point is offset, the puncture forces and energies are significantly reduced. 

The calculated puncture mode for the 25-inch vertical offset side impact analyses is shown in 

Figure 170. The puncture behavior looks very similar to the behavior of an offset head impact 

where the damage is concentrated near the top of the impactor and the puncture forms as a flap 

that initiates at this top edge. We see for this 25-inch offset that the failure initiates while only 

the top half of the impactor is significantly interacting with the tank wall. As a result, the forces 

are concentrated at the upper edge and the total force required to initiate the puncture is reduced. 
134

 (a) Idealized Impact (b) Center Impact

 (c) 15-inch offset (d) 25-inch offset

Figure 168. Impact scenarios used in the vertical offset impact analyses.

Figure 169. Comparison of the calculated side impact behavior with vertical offsets.
135

(a) Before puncture (b) Puncture initiation

Figure 170. Calculated puncture behavior for the 25-inch vertical offset side impact.

A summary of the calculated puncture response for all the vertical offset side impact analyses is 

provided in Table 6. The corresponding puncture forces and puncture energies are plotted against 

the vertical offset distance in Figure 171 and Figure 172, respectively. The comparison shows 

that a small vertical offset (10 inches or less) has little effect on the puncture force. However, as 

the offset increases the puncture force drops significantly and a 25-inch offset reduces the 

puncture force by approximately 35 percent. The trends are similar for puncture energies but are 

more pronounced. The 25-inch offset reduces the puncture energy by approximately 60 percent. 

This is because the puncture force reduction is compounded by a corresponding reduction in the 

ram displacement required to develop that force. 

Table 6. Summary of the vertical offset side impact analyses.

Head Impact 

Calculation

Tank 

Type

Tank 

Shell Jacket Impact Conditions

Vertical 

Offset 

(inches)

Internal 

Pressure

(psi)

Puncture 

Force (lbs)

Puncture 

Energy

(ft-lbs)

R13X 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

25 mph

9.55 in. dia. 0.0 100 psi 1,569,000 2,520,000 

R13Y 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

25 mph

9.55 in. dia. -15.0 100 psi 1.287,000 1,400,000 

R13Z 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

25 mph

9.55 in. dia. -25.0 100 psi 990,000 1,000,000 

R14A 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

25 mph

9.55 in. dia. -5.0 100 psi 1,576,000 2,450,000 

R14B 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

25 mph

9.55 in. dia. -10.0 100 psi 1,467,000 2,060,000 

R14C 600 lb Cl 0.981 in

TC128B 

0.119 in

A1011 

25 mph

9.55 in. dia. -20.0 100 psi 1,116,000 1,180,000 
136

Figure 171. Calculated puncture forces for the various vertical offset side impacts.

Figure 172. Calculated puncture energies for the various vertical offset side impacts.

4.6.2 Analysis of Longitudinal Offset Side Impacts

A corresponding set of analyses was performed to investigate the effects of a longitudinal offset 

to the impact point on side impacts. As the impact point move further from the tank center of 

gravity (CG) the tank motions will include more rotation away from the impact as opposed to the 

pure translation when the impact is aligned with the tank CG (center impact). 

The three primary impact conditions analyzed are shown in Figure 173. In addition to the 

reference condition of the center impact, the impact locations with longitudinal offsets of 80-

inches and 160-inches were also considered. All the analyses used a vertical symmetry plane to 

constrain the motions of the tank in a two-dimensional plane. 
137

The initial three analyses used a 15-mph constant velocity impact condition on an unconstrained 

tank. The force-deflection curves for these three analyses are compared in Figure 174. None of 

the tanks are punctured by these impact conditions. However, the larger the longitudinal offset, 

the more easily the tank is pushed out of the way from the path of the impactor. As a result, the 

effect of the longitudinal offset is very similar to the effects of reducing the tank weight. Since 

the tank can be more easily pushed away from the path of the impacting object, the probability of 

a given impactor puncturing the tank will be reduced as the impact point moves further from the 

tank CG. 

(a) Center Hit (b) 80-inch offset (c) 160-inch offset

Figure 173. Various impact locations investigated for unconstrained side impacts.

Figure 174. The effects of longitudinal offsets on unconstrained side impact behavior.
138

The above effects of the offset impact will be reduced as the motions of the tank are more highly 

constrained. A set of additional impact analyses were performed with a longitudinal offset 

impact condition and an impact wall behind the tank to constrain the tank motions. The models 

for the 80-inch and 160-inch offset impacts are shown in Figure 175. Note that the impact wall 

position is also offset by the same distance to remain aligned with the impactor. 

The initial offset impact analyses on the constrained tanks used the 15-mph constant velocity 

impact condition. The comparison of the force-deflection curves for the center, 80-inch offset, 

and 160-inch-offset impact conditions is shown in Figure 176. Overall, the differences in these 

force-deflection curves are relatively small. However, the larger offset distances introduce 

changes to the tank kinematics, and small asymmetry to the impact behavior that results in 

failures at slightly less displacement levels and reduced puncture energies. 

An additional set of offset impact analyses was performed on the constrained tanks using a 25-

mph impact initial condition with the 295,000 lb impactor. The comparison of the forcedeflection curves for the center, 80-inch offset, and 160-inch-offset impact conditions is shown 

in Figure 177. Again, the differences in these force-deflection curves are relatively small. 

However, for the higher impact speed, the response is more dominated by the inertial constraint. 

As the offset distance increases the tank more rapidly moves away from the impact and more of 

the kinematics and interaction with the BC come into play. As a result, the larger offsets cause 

failures at slightly larger displacement levels and increased puncture energies. This is opposite 

the trend produced at the slower 15 mph impacts. 

 (b) 80-inch offset (c) 160-inch offset

Figure 175. Longitudinal offset impact locations investigated for constrained side impacts.
139

Figure 176. Offset impact effects on a constrained tank, constant 15 mph impact.

Figure 177. Offset impact effects on a constrained tank, 25 mph initial velocity impact.
140

5. Impact Analyses on Other Tank Car Designs

5.1 Introduction and Background

One of the significant factors in the puncture resistance of various pressure tank car designs are 

the effects of the commodities that they carry. The vapor pressure and liquid density of EO, 

anhydrous ammonia (AA), and chlorine are plotted as a function of temperature in Figure 178. 

The comparison shows that for a given temperature, AA has a vapor pressure that is 

approximately 25 percent higher than chlorine and EO has a much lower vapor pressure. 

However, EO is unique from these other commodities in that nitrogen padding is used for safety 

considerations. As a result, the typical pressure in an EO tank car during transit is approximately 

50 psi and results primarily from the nitrogen padding applied to the tank for safety 

considerations. 

Figure 178. Comparison of physical properties of common pressure tank car commodities.

The resulting pressure-volume relationships used for tank car impact analyses with the three 

commodities are compared in Figure 179. These assume the tank and lading are at a temperature 

of approximately 75 degrees F and that the associated outage volume is 10.6 percent. As a result, 

the internal tank pressure for all three commodities rapidly increases as the tank relative volume 

approaches a shell full condition (relative volume of 0.896). 
141

Figure 179. Tank pressure-volume relationships for various commodities (10.6% outage).

5.2 Chlorine Tank Cars

The tank design used in the analyses in Sections 3 and 4 of this report is the 105J600 chlorine 

tank car required under the interim rule. The TC128B tank shell is 100 inches in diameter and 

472 inches long with 2:1 ellipsoidal heads. The tank is covered by a 0.119-inch-thick A1011 

jacket with a 4-inch standoff from the tank. In this section, we analyze the puncture performance 

of the 105J500 chlorine tank car which was the standard prior to the interim rule. The difference 

between these two designs is that the 0.981-inch-thick tank shell used in the 105J600 is reduced 

to a 0.777-inch thickness for the 105J500 tank car.

5.2.1 Side Impacts of Chlorine Tank Cars

A series of analyses were performed with the 105J500 chlorine tank car including different size 

and shape impactors (summarized in Table 7), vertically offset impacts (summarized in Table 8), 

and 45-degree oblique impacts (summarized in Table 9). The objective of these analyses was to 

compare the relative puncture performance of the 105J600 chlorine tank car to that of the 

105J500 tank car. 
142

Table 7. Summary of the baseline side impact analyses on the 105J500 tank car

Calculation Tank Type Tank Shell Shell 

Jacket 

Impact 

Conditions

Internal 

Pressure

(psi)

Puncture 

Force (lbs)

Puncture 

Energy

(ft-lbs)

R18A 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

15 mph

6”x6” ram 100 psi 8.860E+05 1.050E+06 

R18B 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

25 mph

12”x12” ram 100 psi 1.561E+06 3.560E+06 

R18C 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

20 mph

9”x9” ram 100 psi 1.289E+06 2.280E+06 

R18D 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

10 mph

3”x3” ram 100 psi 4.670E+05 3.220E+05 

R18E 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

15 mph

3”x6” ram 100 psi 6.770E+05 6.910E+05 

R18F 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

25 mph

3”x12” ram 100 psi 1.036E+06 1.330E+06 

R18G 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

15 mph

5.73 in. dia. 100 psi 7.960E+05 9.040E+05 

R18H 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

20 mph

7.64 in. dia. 100 psi 1.040E+06 1.610E+06 

R18I 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

25 mph

9.55 in. dia. 100 psi 1.209E+06 2.220E+06 

R18J 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

25 mph

11.46 in. dia. 100 psi 1.452E+06 2.930E+06 

R18K 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

25 mph

13.37 in. dia. 100 psi 1.629E+06 3.660E+06 

Table 8. Summary of the vertical offset side impact analyses on the 105J500 tank car.

Head Impact 

Calculation

Tank 

Type

Tank 

Shell Jacket Impact Conditions

Vertical 

Offset 

(inches)

Internal 

Pressure 

(psi)

Puncture 

Force (lbs)

Puncture 

Energy

(ft-lbs)

R18L 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. 0.0 100 psi 1.224E+06 2.190E+06

R18M 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. -15.0 100 psi 9.950E+05 1.000E+06

R18N 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. -25.0 100 psi 7.590E+05 7.000E+05

R18O 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. -5.0 100 psi 1.273E+06 2.020E+06

R18P 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. -10.0 100 psi 1.144E+06 1.350E+06

R18Q 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. -20.0 100 psi 8.510E+05 7.960E+05
143

Table 9. Summary of the 45-degree oblique side impact analyses on the 105J500 tank car

Calculation Tank 

Type

Tank 

Shell

Shell 

Jacket 

Impact 

Conditions

Internal 

Pressure

(psi)

Puncture 

Initiation 

Force (lbs)

Puncture 

Initiation 

Energy (ft-lbs)

R18R 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

18 mph

6”x6” ram 100 psi 4.430E+05 3.850E+05 

R18S 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

25 mph

12”x12” ram 100 psi 6.710E+05 6.830E+05 

R18T 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

25 mph

9”x9” ram 100 psi 5.680E+05 4.570E+05 

R18U 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

10 mph

3”x3” ram 100 psi 3.500E+05 2.350E+05 

R18V 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

15 mph

5.73 in. dia. 100 psi 5.070E+05 4.140E+05 

R18W 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

20 mph

7.64 in. dia. 100 psi 6.320E+05 7.120E+05 

R18X 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

25 mph

9.55 in. dia. 100 psi 7.320E+05 8.820E+05 

R18Y 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

25 mph

11.46 in. dia. 100 psi 8.250E+05 1.200E+06 

R18Z 500 lb Cl 0.777 in

TC128B 

0.119 in

A1011 

25 mph

13.37 in. dia. 100 psi 9.660E+05 1.610E+06 

The normal side impact puncture forces and energies for the 105J500 tank car are compared to 

those of the 105J600 lb tank car for various size and shape impactors in Figure 180 and Figure 

181, respectively. The puncture force comparison shows that the puncture forces for the 105J600 

tank cars are approximately 30 percent greater than for the 105J500 tank cars. This difference is 

slightly greater than expected since the 0.981-inch tank shell is 26 percent greater than the 0.777-

inch tank shell and both have identical 0.119-inch A1011 jackets. The puncture energy 

comparison, shown in Figure 181, indicates that the 105J600 tank car has a roughly 40-50 

percent increase in puncture energy over the 105J500 tank car for the baseline side impacts. 

The offset and 45-degree oblique side impact puncture energies for the 105J500 tank car are 

compared to those of the 105J600 lb tank car in Figure 182 and Figure 183, respectively. The 

vertical offset impact comparison shows that the puncture energies for the 105J600 tank cars 

range between 15-53 percent greater than for the 105J500 tank cars. The puncture energy 

comparison for the 45-degree oblique impacts, shown in Figure 183, indicates that on average 

the 105J600 tank car has a roughly 20 percent increase in puncture energy over the 105J500 tank 

car. 
144

Figure 180. Puncture force comparisons for the 105J500 and 105J600 tank cars.

Figure 181. Puncture energy comparisons for the 105J500 and 105J600 tank cars.
145

Figure 182. Comparison of the offset impact puncture energies 

for the 105J500 and 105J600 tank cars.

Figure 183. Comparison of the 45-degree oblique impact puncture energies 

for the 105J500 and 105J600 tank cars.

A summary of the relative side impact puncture energy of the 105J500 and 105J600 tank cars is 

shown in Figure 184. The summary includes all of the baseline, offset, and oblique impact 

conditions summarized in Figure 181, Figure 182, and Figure 183. Each point on Figure 184

represents the calculated puncture energy for the 105J600 tank car normalized by the 

corresponding puncture energy for the 105J500 tank car under identical impact conditions. The 

individual scenarios result in a range of normalized puncture energies from a minimum of 1.15 to 

a maximum of 1.85 (15-85 percent higher puncture energies). However, the wide range of 

impact scenarios considered results in an average increase in puncture energy of 39 percent for 

the 105J600 over the 105J500 chlorine tank car. 
146

Figure 184. Normalized puncture energy summary for the 105J600 tank cars.

5.2.2 Head Impacts of Chlorine Tank Cars

The head puncture modeling approach was identical to that of the tank side impact puncture 

analyses. The head impacts analyzed matched the NGRTC Test 1 impact condition (i.e., impact 

point offset below the tank head center). As a result, the problem has a symmetry plane running 

vertically through the test specimen. This symmetry plane was used in most of the head impact 

simulations to reduce the model size by one half compared to the full head model. An example 

model of a tank head with the BW impact zone mesh used in the head puncture analyses is 

shown in Figure 185. An example of the impact and puncture behavior for the offset head impact 

on a chlorine tank head design is shown in Figure 186. 

Figure 185. Tank head model and impact zone mesh used for the head impact analyses.
147

 

(a) Initial geometry (b) Puncture behavior

Figure 186. Calculated behavior of a tank head with the offset impact condition. 

A more limited suite of impact conditions was performed on chlorine tank heads compared to the 

side impacts. A set of four impact analyses were performed using different size impactors in 

offset head impacts. The analyses are for 3, 6, 9, and 12-inch square impactors in an offset 

impact condition. A summary of comparative head impact analyses is provided in Table 10. The 

calculated force-deflection behaviors and integrated puncture energy curves for the 105J500 tank 

heads is shown in Figure 187. The behaviors for the 105J600 tank heads were similar but with 

increased impact force levels. 

Table 10. Summary of the impact analyses for chlorine tank heads. 

Head Impact 

Calculation

Tank 

Type

Tank 

Head

Jacket 

or Head 

Shield

Impact 

Conditions

Impactor 

Edge 

Radius

Internal 

Pressure

(psi)

Puncture 

Force (lbs)

Puncture 

Energy

(ft-lbs)

R95A 600 lb Cl 1.1360 

TC128B 

0.500” 

A572-50

15 mph

6”x6” ram 0.50 inch 100 psi 1.347E+06 1.321E+06 

R95B 600 lb Cl 1.1360 

TC128B 

0.500” 

A572-50

25 mph

12”x12” ram 0.50 inch 100 psi 2.325E+06 3.733E+06 

R95C 600 lb Cl 1.1360 

TC128B 

0.500” 

A572-50

20 mph

9”x9” ram 0.50 inch 100 psi 1.857E+06 2.464E+06 

R95D 600 lb Cl 1.1360 

TC128B 

0.500” 

A572-50

10 mph

3”x3” ram 0.50 inch 100 psi 8.110E+05 4.120E+05 

R22A 500 lb Cl 0.8281 

TC128B 

0.500” 

A572-50

15 mph

6”x6” ram 0.50 inch 100 psi 9.530E+05 8.930E+05 

R22B 500 lb Cl 0.8281 

TC128B 

0.500” 

A572-50

25 mph

12”x12” ram 0.50 inch 100 psi 1.509E+06 2.740E+06 

R22C 500 lb Cl 0.8281 

TC128B 

0.500” 

A572-50

20 mph

9”x9” ram 0.50 inch 100 psi 1.227E+06 1.810E+06 

R22D 500 lb Cl 0.8281 

TC128B 

0.500” 

A572-50

10 mph

3”x3” ram 0.50 inch 100 psi 6.280E+05 3.430E+05 
148

The relative head impact puncture energies of the 105J600 normalized to the corresponding 

energies of the 105J500 tank cars is shown in Figure 188. Each point on Figure 188 represents 

the calculated puncture energy for the 105J600 tank head normalized by the corresponding 

puncture energy for the 105J500 tank head under identical impact conditions. The individual 

scenarios result in a range of normalized puncture energies from a minimum of 1.20 for the 

smallest 3-inch impactor to a maximum of 1.73 for the largest 12-inch impactor (20-73 percent

higher puncture energies). The four impact scenarios considered results in an average increase in 

puncture energy of 47 percent for the 105J600 over the 105J500 chlorine tank head. 

Figure 187. Calculated force-deflection behaviors for the 105J500 tank head impacts.

Figure 188. Normalized impact puncture energy summary for the 105J600 tank heads.
149

5.3 Ethylene Oxide Tank Cars

The baseline ethylene oxide (EO) tank car designs analyzed was the 300 lb EO tank car which is 

the most common existing design used for EO shipments. Analyses were also performed to 

evaluate variations on this design that include a proposed increase to a 400 lb design and the 500 

lb design specified under the FRA interim rule. A summary of the tank parameters for these 

analyses are provided in Table 11. 

Table 11. Summary of the ethylene oxide tank car design parameters.

Tank Designation Tank Shell Tank Jacket Combined 

Thickness 

Tank 

Diameter

Jacket 

Standoff

Baseline 105J300W 0.5625” TC-128B 0.119” A1011 0.6815 inch 111.0 inch 1.0 inch

Baseline 105J400W 0.7350” TC-128B 0.119” A1011 0.8540 inch 111.0 inch 1.0 inch

Interim 105J500W 0.9180” TC-128B 0.119” A1011 1.0370 inch 111.0 inch 1.0 inch

Three sets of analyses were performed for each of the tank designs. These include: (1) normal 

side impacts with a variety of different size and shape impactors, (2) vertical offset impacts, and 

(3) oblique side impacts with a variety of different size and shape impactors. The analyses of 

normal side impacts include 3x3, 6x6, 9x9, 12x12, 3x6, and 3x12 rectangular impactors, all with 

a 0.50-inch radius around the edges. Additional impact analyses were performed using 5.73-, 

7.64-, 9.55-, 11.46-, and 13.37-inch diameter round impactors (ram face perimeter lengths of 18, 

24, 30, 36, and 42 inch, respectively). These impactors (shown previously in Figure 69, Figure 

73, and Figure 76) provide a significant amount of variation in impactor size and shape. 

5.3.1 Normal side Impacts of EO Tank Cars

A summary of the normal side impact puncture forces and puncture energies for the baseline 

300, 400, and 500 lb EO tank cars are provided in Figure 189 and Figure 190, respectively. The 

values for the puncture forces and energies are plotted against the ram face characteristic size 

(defined as the square root of the area of the impactor face). The comparison of the baseline EO 

tank car designs show that the puncture forces for the 400 and 500 lb EO tank cars are on 

average 32 percent and 68 percent greater, respectively, than for the baseline 300 lb EO tank. 

Similarly, the puncture energies for the 400 and 500 lb EO tank cars are on average 35 percent

and 98 percent greater, respectively, than for the baseline 300 lb EO tank. As expected, 

increasing the thickness of the commodity tank is an effective method for increasing the puncture 

resistance of a given tank design.
150

Figure 189. Calculated baseline EO tank puncture forces for various size and shape 

impactors.

Figure 190. Calculated baseline EO tank puncture energies for various size and shape 

impactors.

5.3.2 Offset Impacts of EO Tank Cars

The second series of analyses performed for each of the EO tank car designs are the vertical 

offset impacts. The analyses were performed using conditions identical to those for the chlorine 

tank car described previously. The vertical offset side impact analyses were performed using the 

9.55-inch-diameter round impactor. 

A summary of the puncture forces and puncture energies for the various EO tank car designs are 

plotted against the vertical offset distance in Figure 171 and Figure 172, respectively. The 
151

comparison shows that a small vertical offset (10 inches or less) has little effect on the puncture 

force. However, as the offset increases the puncture force drops significantly and a 25-inch offset 

reduces the puncture force by approximately 25 percent. The trends are similar for puncture 

energies but are more pronounced. The 25-inch offset reduces the puncture energy by 

approximately 60 percent. This is because the puncture force reduction is compounded by a 

corresponding reduction in the ram displacement required to develop that force. 

Figure 191. Calculated puncture forces for the various vertical offset side impacts.

Figure 192. Calculated puncture energies for the various vertical offset side impacts.
152

5.3.3 Oblique Impacts of EO Tank Cars

In addition to the above normal and offset side impact analyses, a set of analyses was performed 

with the full range of impactor sizes and shapes at a 45-degree oblique impact angle. The impact 

scenario is shown in Figure 193. 

Figure 193. Impact scenario for the 45-degree oblique side impact analyses.

Comparisons of the normal and oblique impact puncture forces and energies are provided in 

Figure 194 and Figure 195 for the baseline 300 lb, 400 lb, and 500 lb EO tank cars. The oblique 

puncture forces are approximately 50 percent of the normal puncture forces for the largest 

impactors. However, as the impactor size is reduced the differences in puncture force are also 

reduced. At the smallest 3x3 inch impactor there is very little difference between the normal and 

oblique impact puncture forces. As a result, a linear fit to the oblique puncture force data would 

not intercept the origin of the graph as used in the normal impact data. 

Figure 194. Comparison of puncture forces for normal and oblique impacts.
153

Figure 195. Comparison of puncture energies for normal and oblique impacts.

The puncture energies for the oblique impact show similar trends to the puncture forces. The 

puncture energies for the largest impactors are reduced by approximately 70 percent. Again, as 

the impactor size is reduced the differences in puncture energies are also reduced. For the 3x3 

inch impactor there is much less difference between the normal and oblique impact puncture 

energies. 

5.3.4 Summary of EO Tank Shell Puncture Performance

The full sets of normal, offset, and oblique impact analyses were performed for all three of the 

EO tank designs listed in Table 11. Thus, we have 26 different impact conditions analyzed for 

each of the EO tank designs. In this section, we summarize the relative puncture performance for 

the various designs. 

To assess the relative puncture performance of different designs, we compare the puncture 

energy for each design under the same impact conditions. In this comparison, we normalize the 

puncture performance of each of the various designs to the baseline 300 lb EO tank car. Using 

this approach, the relative performance of the baseline 400 lb and 500 lb EO tank cars are 

summarized in Figure 196. Each of the symbols in Figure 196 represents the calculated puncture 

energy from one of the 26 impact scenarios divided by the corresponding puncture energy from 

the baseline 300 lb EO tank car for the same impact scenario. In addition to the puncture energy 

data from each of the calculations, an average value line for all 26 impact scenarios is added to 

the graph for each design. The comparison shows that the 400 lb tank car has on average a 34

percent higher puncture energy than the 300 lb EO tank car for the set of impact conditions 

analyzed. Similarly, the puncture energies for the 500 lb EO tank car are approximately double 

those of the 300 lb EO car for these impacts. 

An alternative comparison is to compare the performance of the EO tank designs with the 

chlorine tank designs. For this comparison, the results of the normal and 45-degree oblique side 

impact analyses were used (20 analyses for each design). The puncture energy of each of the EO 

tank designs was normalized to the puncture energy for the 105J500 chlorine tank car. These 
154

normalized puncture energies are shown in Figure 197. For comparison the normalized puncture 

energies for the 105J600 chlorine tank car are added to the graph. In this comparison, the 

puncture energies for the 105J500W EO tank car design are considerably higher than those of the 

105J600W chlorine tank car. The EO tanks have relatively high puncture energies as a result of 

the lower tank pressures and larger diameter tanks. The 105J500W, 105J400W, and 105J300W 

EO tank cars have puncture energies on average 82 percent higher, 17 percent higher, and 12 

percent lower, respectively, than the 105J500W chlorine tank car. The corresponding puncture 

energies for the 105J600W chlorine tank car were on average 37 percent higher than the 

105J500W chlorine tank car. 

Figure 196. Comparison of relative puncture performance of the baseline EO tank designs.

Figure 197. Comparison of relative puncture performance of EO and chlorine tank designs.
155

5.3.5 Head Impacts of EO Tank Cars

A suite of impact analyses was performed on the various EO tank head designs. For each design, 

a set of four impact analyses were performed using different size impactors in offset head 

impacts. A summary of comparative head impact analyses is provided in Table 12. 

The relative side impact puncture energy of the 400 lb and interim 500 lb EO tank heads

normalized to the corresponding energies of the legacy 300 lb tank head is shown in Figure 198. 

Each point represents the calculated puncture energy for the 400 or 500 lb tank head normalized 

by the corresponding puncture energy for the 300 lb tank head under identical impact conditions. 

The four impact scenarios considered results in an average increase in puncture energy of 37 

percent and 49 percent for the 400 lb and 500 lb heads, respectively, over the 300 lb EO tank 

head. 

In an alternative comparison, the relative head impact puncture energy of the 300, 400, and 500 

lb EO tank heads are normalized to the corresponding energies of the legacy 105J500 chlorine 

tank heads, as shown in Figure 199. The four impact scenarios considered result in an average 

decrease in puncture energy of 18 percent for the 300 lb EO tank head relative to the 500 lb

chlorine tank head. The 400 lb and 500 lb EO tank heads have an average increase in puncture 

energy of 10 percent and 22 percent, respectively, over the 500 lb chlorine tank head. 

Table 12. Summary of the impact analyses for EO head impacts. 

Head 

Impact 

Calculation

Tank 

Type

Tank 

Head

Jacket 

or Head 

Shield

Impact 

Conditions

Impactor 

Edge 

Radius

Internal 

Pressure

(psi)

Puncture 

Force (lbs)

Puncture 

Energy

(ft-lbs)

R29A 500 lb EO 0.9784 

TC128B 

0.500” 

A572-50

15 mph

6”x6” ram 0.50 inch 50 psi 1.191E+06 1.258E+06 

R29B 500 lb EO 0.9784 

TC128B 

0.500” 

A572-50

25 mph

12”x12” ram 0.50 inch 50 psi 1,721,000 2.689E+06 

R29C 500 lb EO 0.9784 

TC128B 

0.500” 

A572-50

20 mph

9”x9” ram 0.50 inch 50 psi 1.49E+06 2.24E+06 

R29D 500 lb EO 0.9784 

TC128B 

0.500” 

A572-50

10 mph

3”x3” ram 0.50 inch 50 psi 7.31E+05 4.28E+05 

R2BA 400 lb EO 0.8500 

TC128B 

0.500” 

A572-50

15 mph

6”x6” ram 0.50 inch 50 psi 1.02E+06 1.13E+06 

R2BB 400 lb EO 0.8500 

TC128B 

0.500” 

A572-50

25 mph

12”x12” ram 0.50 inch 50 psi 1,390,000 1.964E+06

R2BC 400 lb EO 0.8500 

TC128B 

0.500” 

A572-50

20 mph

9”x9” ram 0.50 inch 50 psi 1.287E+06 1.988E+06 

R2BD 400 lb EO 0.8500 

TC128B 

0.500” 

A572-50

10 mph

3”x3” ram 0.50 inch 50 psi 6.730E+05 4.050E+05 

R2AA 300 lb EO 0.6030 

TC128B 

0.500” 

A572-50

15 mph

6”x6” ram 0.50 inch 50 psi 6.83E+05 7.04E+05 

R2AB 300 lb EO 0.6030 

TC128B 

0.500” 

A572-50

25 mph

12”x12” ram 0.50 inch 50 psi 1.048E+06 2.381E+06 

R2AC 300 lb EO 0.6030 

TC128B 

0.500” 

A572-50

20 mph

9”x9” ram 0.50 inch 50 psi 8.840E+05 1.488E+06 

R2AD 300 lb EO 0.6030 

TC128B 

0.500” 

A572-50

10 mph

3”x3” ram 0.50 inch 50 psi 5.060E+05 3.320E+05 
156

Figure 198. Normalized impact puncture energy summary for the 400 lb and 500 lb EO

tank heads. 

Figure 199. Normalized impact puncture energy summary for various EO tank heads.

5.4 Anhydrous Ammonia Tank Cars 

The baseline anhydrous ammonia (AA) tank car designs analyzed was the 340 lb AA tank car 

which is a common existing design used for AA shipments. Analyses were also performed to 

evaluate the 500 lb design specified under the FRA interim rule. A summary of the tank 

parameters for these analyses are provided in Table 13. 
157

Table 13. Summary of the anhydrous ammonia tank car design parameters.

Tank Designation Tank Shell Tank Jacket Combined 

Thickness 

Tank 

Diameter

Jacket 

Standoff

Baseline 112J340W 0.6250” TC-128B 0.119” A1011 0.7440 inch 111.0 inch 1.0 inch

Interim 112J500W 0.9180” TC-128B 0.119” A1011 1.0370 inch 111.0 inch 1.0 inch

Two sets of analyses were performed for each of the tank designs. These include the normal side 

impacts and the 45-degree oblique side impacts with a variety of different size and shape 

impactors. The impactors include the 3x3, 6x6, 9x9, 12x12, 3x6, and 3x12 rectangular impactors 

and the 5.73-, 7.64-, 9.55-, 11.46-, and 13.37-inch diameter round impactors. These impactors 

(shown previously in Figure 69, Figure 73, and Figure 76) provide a significant amount of 

variation in impactor size and shape. 

5.4.1 Normal side Impacts of AA Tank Cars

A summary of the normal side impact puncture forces and puncture energies for the baseline 340 

and 500 lb AA tank cars are provided in Figure 200 and Figure 201, respectively. The values for 

the puncture forces and energies are plotted against the ram face characteristic size defined as the 

square root of the area of the impactor face. The comparison of the baseline AA tank car designs 

shows that the puncture forces for the 500 lb AA tank cars are on average approximately 40

percent greater than for the baseline 340 lb AA tank. Similarly, the puncture energies for the 500 

lb AA tank cars are on average 85 percent greater than for the baseline 340 lb AA tank. As 

expected, increasing the thickness of the commodity tank is an effective method for increasing 

the puncture resistance of the tank design.

Figure 200. Calculated baseline AA tank puncture forces for various size and shape 

impactors.
158

Figure 201. Calculated baseline AA tank puncture energies for various size and shape 

impactors.

5.4.2 Oblique Impacts of AA Tank Cars

In addition to the above normal side impact analyses, a set of analyses was performed with the 

full range of impactor sizes and shapes at a 45-degree oblique impact angle. The impact scenario 

is the same as used for the EO tank cars, shown previously in Figure 130. Comparisons of the 

normal and oblique impact puncture forces and energies are provided in Figure 202 and Figure 

203 for the baseline 340 lb and 500 lb AA tank cars. 

Figure 202. Comparison of puncture forces for normal and oblique impacts.

The oblique puncture forces are approximately 50 percent of the normal puncture forces for the 

largest impactors. However, as the impactor size is reduced the differences in puncture force are 
159

also reduced. At the smallest 3x3 inch impactor there is very little difference between the normal 

and oblique impact puncture forces. As a result, a linear fit to the oblique puncture force data 

would not intercept the origin of the graph as used in the normal impact data. 

Figure 203. Comparison of puncture energies for normal and oblique impacts.

The puncture energies for the oblique impact show similar trends to the puncture forces. The 

puncture energies for the largest impactors are reduced by approximately 60 percent. Again, as 

the impactor size is reduced the differences in puncture energies are also reduced. For the 3x3 

inch impactor there is much less difference between the normal and oblique impact puncture 

energies. 

5.4.3 Summary of AA Tank Shell Puncture Performance

The full sets of normal and oblique impact analyses were performed for both of the AA tank 

designs listed in Table 13. Thus, we have 20 different impact conditions analyzed for both of the 

AA tank designs. In this section, we summarize the relative puncture performance for the various 

designs. 

The performance of the AA tank designs is compared to the chlorine tank designs in Figure 204. 

For this comparison, the results of the normal and 45-degree oblique side impact analyses were 

used (20 analyses for each design). The puncture energy of each of the AA tank designs was 

normalized to the puncture energy for the 105J500W chlorine tank car. For comparison the 

normalized puncture energies for the 105J600W chlorine tank car are added to the graph. The 

112J500W and 112J340W AA tank cars are on average 10 percent above and 39 percent below 

the 105J500W chlorine tank car, respectively. The puncture energies for the 105J600W chlorine 

tank car were on average 37 percent higher than the 105J500W chlorine tank car. 
160

Figure 204. Comparison of relative puncture performance of AA and chlorine tank designs.

5.4.4 Head Impacts of AA Tank Cars

A suite of impact analyses was performed on the legacy 340 lb and interim 500 lb AA tank head 

designs. For each design, a set of four impact analyses were performed using different size 

impactors in offset head impacts. A summary of comparative head impact analyses is provided in 

Table 14. 

Table 14. Summary of the impact analyses for AA head impacts. 

Head 

Impact 

Calculation

Tank 

Type

Tank 

Head

Jacket 

or Head 

Shield

Impact 

Conditions

Impactor 

Edge 

Radius

Internal 

Pressure

(psi)

Puncture 

Force (lbs)

Puncture 

Energy

(ft-lbs)

R44A 500 lb AA 0.9784 

TC128B 

0.500” 

A572-50

15 mph

6”x6” ram 0.50 inch 125 psi 1.115E+06 1.047E+06 

R44B 500 lb AA 0.9784 

TC128B 

0.500” 

A572-50

25 mph

12”x12” ram 0.50 inch 125 psi 1.816E+06 2.505E+06 

R44C 500 lb AA 0.9784 

TC128B 

0.500” 

A572-50

20 mph

9”x9” ram 0.50 inch 125 psi 1.446E+06 1.786E+06 

R44D 500 lb AA 0.9784 

TC128B 

0.500” 

A572-50

10 mph

3”x3” ram 0.50 inch 125 psi 6.880E+05 3.530E+05 

R45A 340 lb AA 0.6720 

TC128B 

0.500” 

A572-50

15 mph

6”x6” ram 0.50 inch 125 psi 7.950E+05 6.410E+05 

R45B 340 lb AA 0.6720 

TC128B 

0.500” 

A572-50

25 mph

12”x12” ram 0.50 inch 125 psi 1.280E+06 1.626E+06 

R45C 340 lb AA 0.6720 

TC128B 

0.500” 

A572-50

20 mph

9”x9” ram 0.50 inch 125 psi 8.100E+05 1.173E+06 

R45D 340 lb AA 0.6720 

TC128B 

0.500” 

A572-50

10 mph

3”x3” ram 0.50 inch 125 psi 5.200E+05 2.380E+05 

The relative head impact puncture energy of the interim 500 lb AA tank heads normalized to the 

corresponding energies of the legacy 340 lb tank head is shown in Figure 205. Each point 
161

represents the calculated puncture energy for the 500 lb tank head normalized by the 

corresponding puncture energy for the 340 lb tank head under identical impact conditions. The 

four impact scenarios considered results in an average increase in puncture energy of 54 percent

over the 340 lb AA tank head. 

In an alternative comparison, the relative head impact puncture energy of the 340 and 500 lb AA 

tank heads are normalized to the corresponding energies of the legacy 105J500 chlorine tank 

head, as shown in Figure 206. The four impact scenarios considered result in an average decrease

in puncture energy of 34 percent for the 340 lb AA tank head relative to the 500 lb chlorine tank 

head. The 500 lb AA tank head had an average increase in puncture energy of 3 percent over the 

500 lb chlorine tank head. 

Figure 205. Normalized impact puncture energy summary for the 500 lb AA tank head. 

Figure 206. Normalized impact puncture energy summary for various AA tank heads.
162

5.5 Comparison of the Various Pressure tank Car designs

The full set of normal and 45-degree oblique side impacts were performed for all the chlorine, 

EO, and AA tank car designs considered. A comparison of the puncture energies for the normal 

impacts of the various tank cars are compared in Figure 207. The designs include 500 and 600 lb 

chlorine tank cars, 340 and 500 lb AA tank cars, and 300, 400, and 500 lb EO tank cars. The 

112J340W AA tank car has the lowest puncture energies. The 105J300W EO tank car has the 

second lowest puncture energies. However, the puncture energies for the 105J300W EO tank car 

are on average approximately 50 percent higher than the 112J340W AA tank car and only 15

percent lower than the 105J500W chlorine tank car. The puncture energies for the 105J400W EO 

tank car are on average 20 percent greater than the 105J500W chlorine tank car and 10 percent

higher than the 112J500W AA tank car. The puncture energies for the 105J500W EO tank car 

are the highest for any of the designs analyzed and on average 10 percent greater than the 

105J600W chlorine tank car. 

For a further comparison of the various designs, we added the results of the oblique impacts to 

the normal impacts and normalized all of the various designs to the puncture energies of the 

105J500W chlorine tank car. The comparison for these normalized results is provided in Figure 

208. In this comparison, the puncture energies for the 105J500W EO tank car are considerably 

higher than for any of the other tank car designs. The 105J400W EO tank car puncture 

performance is above the 112J500W AA tank car and below 105J600W chlorine tank car. 

Figure 207. Comparison of relative puncture performance of various tank cars.
163

Figure 208. Relative side impact puncture performance of various tank designs.

A similar comparison for the normalized impact resistance in head impacts for the various tank 

designs is provided in Figure 209. In this comparison, the puncture energies for the 105J600W 

chlorine tank car are higher than for any of the other tank car designs. The 105J600W chlorine 

tank head was also somewhat unique in that the relative puncture resistance was much better for 

the largest impactors and showed significantly less improvement for the smallest impactor. The 

105J400W EO tank car puncture performance is above the 112J500W AA tank car and below 

105J600W chlorine tank car. 

Figure 209. Relative head impact puncture performance of various tank designs.
164

5.6 DOT Class 111 tank cars

There have been ongoing activities in the tank car community to address safety of generalpurpose tank cars. These activities were summarized in the FRA October 2011 regulatory update 

(FRA, 2011). The background information from that update is summarized below.

On March 9, 2011, the Association of American Railroads (AAR), on behalf of its members and 

the Tank Car Committee (TCC), jointly petitioned the Pipeline and Hazardous Materials Safety 

Administration (PHMSA) and Transport Canada (TC) to establish new standards for DOT Class 

111 tank cars used to transport hazardous materials in packing groups I and II. The petition (P1577), which was an outgrowth of a TCC executive working group, proposed new construction 

standards and specifically recommended no modification for existing tank cars. The AAR agreed 

to forward the petition to PHMSA on behalf of the TCC as a result of a unanimous decision by 

the Committee.

On May 10, 2011, FRA met with the Railway Supply Institute’s (RSI) Tank Car Safety 

Committee to discuss improvements to tank cars used for the transportation of crude oil in unit 

trains. FRA requested this meeting to discuss improving tank car safety specific to crude oil tank 

cars given the recent increase in demand for these cars. The intent of the meeting was to spur 

discussion about innovative solutions that improve tank car safety for future changes in the 

hazardous materials transportation supply chain. The meeting resulted in the RSI members 

offering to develop an industry standard (non-regulatory) in collaboration with the AAR, the 

Renewable Fuels Association (RFA), Growth Energy, and the American Petroleum Institute 

(API). This effort is being conducted through a TCC Task Force led by the FRA.

On June 15, 2011, an Industry Consortium consisting of RSI, AAR, API, Growth Energy and the 

RFA submitted an action plan for the continuous reduction of risk associated with rail 

transportation of Crude Oil classified as PG I and II and Ethanol. The objectives of the action 

plan are to: (1) make recommendations on derailment risk reduction actions that can be quickly 

implemented; and (2) develop a new specification for tank cars transporting the aforementioned 

commodities and allowance for new cars for these services to be constructed to the standard 

proposed in P-1577. The Industry Consortium met with the FRA on July 12, 2011, to review the 

plan. The FRA concurred with the objectives and supported the proposed approach.

On July 20, 2011, at the summer AAR Tank Car Committee meeting docket T87.6 was created 

with a dual charge to develop an industry standard for tank cars used to transport crude oil, 

denatured alcohol, and ethanol/gasoline mixtures; as well as to consider operating requirements 

to reduce the risk of derailment of tank cars carrying Crude Oil classified as PG I and II, and 

Ethanol. The task force has been organized into two separate working groups; the first referred to 

as the design working group, and the second referred to as the operations working group. The 35-

member design working group has met three times, August 17, September 9, and September 23 

and has made significant progress. 

The overarching objective of the working group is to maximize benefits, in this case safety, 

while minimizing cost. The working group is evaluating numerous design features intended to 

improve the survivability in accidents of tank cars transporting the referenced commodities. 

These features will include the new AAR standards outlined in CPC-1230 and petition P-1577, 

which is currently under review with PHMSA. The additional features will be considered that are 

based on the findings of forensic evaluations of recent derailments involving tank cars built for 

ethanol service. The segments of the industry represented in the working group all define cost 
165

differently. The tank car builders/owners define cost in terms of manufacturability, utilization 

(limited number of commodities), and suitability of design (retrofit requirements to comply with 

changing regulations). The railroads define cost in terms of imposed operating requirements. The 

shippers define cost in terms of loss of capacity and compatibility with existing facility and 

railroad infrastructure.

The analyses described in this section of the report are in support of these T87.6 activities. The 

objective is to assess the relative puncture performance of existing and proposed designs. The 

properties of the specific designs analyzed are summarized in Table 15. The initial three designs 

analyzed were: (1) a baseline 111A100W1 tank car with a 7/15-inch A516-70 tank shell, (2) a 

CPC-1230 and P-1577 proposed design with a 0.5-inch TC128B tank shell, and (3) a proposed 2-

layer concept that had a 3/8-inch TC128B Tank shell with a 1/4-inch jacket. However, for 

comparison, jacketed versions of the first two designs were added and a final design that 

considered the 3/8-inch shell and 1/4-inch jacket combined into a single monolithic 5/6-inch 

TC128B tank shell. 

The DOT-117A100W tank car specification did not exist at the time of the original research 

project in 2013 (Kirkpatrick, 2013), and evaluation of the DOT-117 was outside the scope of this 

effort. However, the parameters for the DOT-117 tank car are included in Table 15 for 

comparison. Based on the comparison of parameters in Table 15 the DOT-117 design is similar 

to the jacketed P1577/CPC1230 tank car design but with an additional 1/16-inch thickness in the 

tank shell. Thus, we would expect additional puncture resistance above the levels obtained for 

that design. 

Table 15. Summary of the general-purpose tank car design parameters.

Tank Designation Tank Shell Tank Jacket Combined 

Thickness 

Tank 

Diameter

Jacket 

Standoff

DOT-111A100W1 7/16” A516-70 N/A 0.4375 inch 111.0 inch 1.0 inch

DOT-111A100W3 7/16” A516-70 0.119 in A1011 0.5565 inch 111.0 inch 1.0 inch

P1577/CPC1230 0.5 in TC-128B N/A 0.5000 inch 111.0 inch 1.0 inch

P1577/CPC1230(1) 0.5 in TC-128B 0.119 in A1011 0.6190 inch 111.0 inch 1.0 inch

Concept 1 (2-Layer)(2) 3/8” TC-128B 1/4” TC-128B 0.6250 inch 111.0 inch 1.0 inch

Concept 2 (Monolithic) 5/8” TC-128B N/A 0.6250 inch 111.0 inch 1.0 inch

DOT-117A100W 9/16” A516-70 0.119 in A1011 0.6815 inch 111.0 inch 1.0 inch

Notes: (1) Note that the CPC-1230/P-1577 proposed design allows for a reduced 7/16-inch TC128B tank 

shell when a jacket is used. However, for these analyses the full 0.5-inch tank thickness was 

maintained to achieve a combined thickness that is roughly equivalent to the concept 1 and 2

designs. 

(2) The 3/8-inch tank thickness is less than the minimum allowable under current regulations (7/16-

inch). However, it was included to generate a hypothetical 2-layer design with a total combined 

thickness close to other designs. 
166

5.6.1 Effects of Outage Volume

The general-purpose tank cars carry commodities in an unpressurized or low-pressure condition. 

However, with many of the commodities they carry they can typically operate with relatively 

low outage volumes. As a result, significant pressures can develop as an impactor dents the tank 

car and reduces the tank volume. A series of analyses were performed on a general-purpose car 

to analyze the effects of this outage volume and it was found to be a significant factor for the 

impact response (Kirkpatrick, 2010). The results of these analyses are summarized in this 

section. 

The outage volume effects analyses were performed on an unpressurized DOT-111A100W1 tank 

car (no jacket). The specific geometry modeled is a 24,000-gallon tank shown in Figure 210. The 

tank is 111-inches in diameter with a 44-foot 7-inch-long cylindrical shell and 2:1-ellypsoidal 

heads. The tank is constructed with a 0.4375-inch-thick A516-70 steel tank shell. The tanks are 

impacted by the standard 6x6 inch impactor (286,000 lbs) at a speed of 16.2 mph. 

(a) Quarter-symmetry model of tank, ram, and reaction wall

(b) Mesh resolution of the tank and impact patch

Figure 210. Model of a 23,000-gallon DOT-111A100W tank for analysis of outage volume 

effects.
167

The tanks in the analyses were modeled as initially unpressurized with a control volume 

algorithm used to include the pressure-volume effects. Control volume curves were generated

representative of a tank filled with an incompressible liquid to various levels up to as much as 99 

percent of the tank capacity (1 percent outage). The control volume pressure curves (gauge 

pressure) for outage volumes between 1 and 18 percent are shown in Figure 211 and are 

generated assuming the outage volume contains an ideal gas initially at one atmosphere (absolute 

pressure). 

Figure 211. Control volume pressure curves for various outages between 1 and 18 percent.

A comparison of the impact deformations at the point of the tank shell penetration (puncture) for 

the 1, 3, and 9 percent outage volumes are shown in Figure 212. The comparison clearly shows 

that the larger outage volumes allow for a larger ram displacement before the tank is punctured. 

The comparison of the corresponding force-deflection behaviors and puncture energies with the 

different outage volumes is shown in Figure 213. A summary of the results from all the 

calculations is provided in Table 16. The comparison shows that tanks with outage volumes 

between 1 and 18 percent percent are punctured at similar force levels (392,000 to 467,000 lbs) 

but at significantly different displacements (16 to 65 inches) resulting in puncture energies 

between 256,000 and 1,370,000 ft-lbs. 
168

 

(a) Deformation at puncture for 1% outage

 

(b) Deformation at puncture for 3% outage

 

(c) Deformation at puncture for 9% outage

Figure 212. Calculated impact and puncture behaviors for different outage volumes.
169

Figure 213. Force-deflection curves and puncture energies for different outage volumes.

Table 16. Summary of impact analyses to assess outage volume effects. 

Outage 

Volume Tank Shell Impact Conditions

Ram Puncture 

Displacement

Puncture 

Force (lbs)

Puncture 

Energy

(ft-lbs)

Pressure at 

Puncture

1 % 0.4375 in

A516-70

16.2 mph

6”x6” ram 16 inches 467,000 256,000 178 psi

2 % 0.4375 in

A516-70

16.2 mph

6”x6” ram 25 inches 464,000 474,000 89 psi

3 % 0.4375 in

A516-70

16.2 mph

6”x6” ram 28 inches 452,000 537,000 53 psi

6 % 0.4375 in

A516-70

16.2 mph

6”x6” ram 36 inches 439,000 715,000 29 psi

9 % 0.4375 in

A516-70

16.2 mph

6”x6” ram 42 inches 428,000 825,000 22 psi

12 % 0.4375 in

A516-70

16.2 mph

6”x6” ram 47 inches 415,000 935,000 18 psi

15 % 0.4375 in

A516-70

16.2 mph

6”x6” ram 53 inches 410,000 1,075,000 17 psi

18 % 0.4375 in

A516-70

16.2 mph

6”x6” ram 65 inches 392,000 1,370,000 21 psi

100 % 0.4375 in

A516-70

16.2 mph

6”x6” ram >110 inches n/a >1,800,000 n/a 

The calculated control volume pressures in the various analyses are compared in Figure 214 and 

the corresponding pressures at the time of tank puncture are included in Table 16. As expected, 

the displacement required to develop an internal pressure increase is significantly larger for the 

larger outage volumes. Another interesting finding is that the calculated pressure levels at the 

point of the tank puncture is significantly reduced for the larger outage volumes. Thus, the 
170

fraction of the impact force resulting from the impact deformations is larger as the puncture 

deformation is increased and the effects of increasing the outage volume would be expected to 

have a diminishing return. 

Figure 214. Control volume pressures for impacts with different outage volumes.

The calculated puncture energies are plotted against the outage volume in Figure 215. Also 

included in the figure is an approximate fit to the calculated energies. The functional form of the 

fit is a puncture energy that is proportional to the square root of the outage volume. Thus, the 

effect of an incremental increase of the outage volume results in a corresponding smaller 

increase in the puncture energy as the outage volume grows larger. 

The calculated puncture energies have some natural variability about the functional fit. This 

variability can be seen by considering the impact behavior of an empty tank as shown in Figure 

216. In the empty tank analysis, the impactor dents the side of the tank, and the dent continues to 

grow until the impactor eventually impacts the far side of the tank and impact wall (greater than 

110-inch dent depth. As the side of the tank collapses the resistance of the tank dent oscillates 

between 150,000 and 300,000 lbs as the dent grows. The timing of the puncture for the different 

outage levels would be influenced by these natural variations in the impact resistance and as a 

result the calculated puncture energies do not fall directly on the smooth functional fit. 
171

Figure 215. Effect of the outage volume on the puncture energy in side impacts.

Figure 216. Force-deflection curve and impact energy dissipation for an empty tank.

An inspection of the puncture results in Table 16 indicates a trend of modest reduction in the 

puncture force as the outage volume is increased. The mechanisms believed responsible for this 

is the uniformity of the stresses around the edge of the impact face. The profile of the impact 

damage during the indentation process for both the 1 and 18 percent outage calculations is shown 

in Figure 217. When the tank has a 1 percent outage volume the damage development is 

relatively uniform around the perimeter of the contact patch other than the slight concentrations 

of damage at the corners of the impact face. However, for the 18 percent outage the damage 

along the top and bottom of the impact face is greater than that along the sides of the impactor. In 

addition, the larger dent depths would allow for more plastic bending around the edges and 

corners of the impact face which could result in a less uniform stress state and damage 

development through the thickness of the tank wall. 
172

(a) Damage Profile for 1% outage (b) Damage Profile for 18% Outage

Figure 217. Side impact damage distribution for 1% and 18% outage volumes.

5.6.2 Analyses of Different General Purpose Tank Designs

The various general purpose tank car designs, listed in Table 15, were each analyzed with a suite 

of various size and shape impactors. The baseline analyses include the 3x3, 6x6, 9x9, 12x12, and 

3x12 rectangular impactors as well as the 5.73-, 7.64-, 9.55-, 11.46-, and 13.37-inch diameter 

round impactors. The initial analyses used the 1 percent outage volume since it was the most 

critical tank condition. 

The summary of the puncture forces for the various tank designs is shown in Figure 218. There is 

an approximately 40 percent increase in the puncture forces for the strongest tank designs 

(Concepts 1 & 2 and jacketed CPC1230/P1577) compared to the weakest tank design 

(111A100W1). However, these strong tank car designs have approximately 40 percent more steel 

in the tank and jacket than the baseline 111A100W1 design. 

Figure 218. Correlation of the side impact puncture forces with the impactor characteristic 

size.
173

To eliminate the tank thickness effect, the puncture forces were normalized by dividing them by 

the combined tank and jacket thickness, shown in Figure 219. Although there is still some 

variation in the designs, the correlation of normalized puncture force and impactor size between 

designs is much closer. Some of the variation in the normalized puncture forces for the various 

designs comes from the difference between single and two-layer (jacketed) systems. In the twolayer systems the layers can puncture sequentially. If the sequential failures occur at significantly 

different levels of deformation, the puncture protection is not optimized, and the normalized 

puncture force is lower than would be achieved by a similar single layer system. 

A summary of the puncture energies for the various general purpose tank designs is shown in 

Figure 220. The comparison shows that there is an approximately 70 percent increase in the 

puncture energies for the strongest tank designs (Concepts 1&2) compared to the weakest tank 

design (111A100W1). In addition, these improvements are greater than the 40 percent more steel 

in the Concept 1 & 2 tank designs compared to the baseline 111A100W1 design. The puncture 

energies for the jacketed CPC1230/P1577 design (with the 0.5-inch TC128B tank shell) are only 

about 10 percent lower than the Concept 2 design. 

Figure 219. Comparison of the normalized side impact puncture forces.

The puncture energies in Figure 220 show a correlation that is roughly linear with the 

characteristic size of the impactor. This is in contrast with the comparison of impact energies for 

the 600 lb chlorine tank car, shown previously in Figure 80, where the shape of the puncture 

energy correlation is more closely represented by the square of the characteristic size of the 

impactor. 
174

Figure 220. Correlation of the side impact puncture energies with the ram face 

characteristic size.

The differences in the puncture energy correlations of the 600 lb chlorine and general-purpose 

tank cars can be seen by a comparison of the response measures. The force deflection curves for 

the 105J600 and 111A100W3 tank cars and the 3-, 6-, 9-, and 12-inch square impactors are 

compared in Figure 221. For the 105J600 tank car the ram displacement at puncture is 

approximately linearly proportional to the puncture forces (and therefore the impactor 

characteristic size). The 3-inch impactor punctures at approximately 18 inches of ram 

displacement and the 12-inch impactor punctures at 55 inches of displacement. However, for the 

general-purpose tank car, the shape of the force deflection curves shows a response that becomes 

significantly steeper as the displacement increases and, as a result, the corresponding growth in 

the puncture displacements is reduced. The 3-inch impactor punctures at approximately 21 

inches of ram displacement and the 12-inch impactor punctures at 28 inches of displacement 

with the 111A100W3 general purpose tank car. 

A major effect controlling these behaviors of the chlorine and general-purpose tank cars is the 

initial pressure combined with the pressure buildup as the impactor dents the tank. The pressure 

displacement curves for the 105J600 and 111A100W3 tank cars and various rectangular 

impactors are compared in Figure 222. For the 105J600 tank car the initial pressure was 100 psi. 

The initial pressure helps to increase the initial stiffness of the tank. In addition, the pressure 

does not increase significantly until approximately 30-40 inches of ram displacement where the 

10.6 percent outage volume starts to be significantly reduced. Only the 9- and 12-inch impactors 

puncture at pressures that are well above the initial pressure (160 and 210 psi respectively for the 

9- and 12-inch impactors). 

The internal pressure effects are significantly different for the 111A100W3 tank cars. These 

general-purpose tank cars were initially unpressurized resulting in a more compliant tank car. 

However, the pressure begins to build up significantly after approximately 15 inches of ram 

displacement as a result of the much smaller 1 percent outage volume. All the general-purpose 

tank car analyses are influenced by the buildup of pressure within the tank. The pressure at burst 

is approximately 25 psi for the 3-inch impactor and increases steadily to approximately 180 psi 
175

for the 12-inch impactors. The effects of these pressures can be compared to the shape of the 

force-deflection curve for the empty general purpose tank car shown in Figure 216, where the 

indentation force remains low. 

(a) 105J600 chlorine tank car

(b) 111A100W3 general purpose tank car

Figure 221. Calculated force-deflection curves for the 105J600 and 111A100W3 tank cars.
176

(a) 105J600 chlorine tank car

(b) 111A100W3 general purpose tank car

Figure 222. Calculated pressure-deflection curves for the 105J600 and 111A100W3 tank 

cars.

The above analyses were all performed for the assumed worst-case scenario of a 1 percent

outage volume. However, it is desirable to also compare the trends to see if the conclusions hold 

for a more typical outage volume. To investigate this effect an additional set of analyses was 

performed with the outage volume increased to 3 percent. The analyses were performed for the 

jacketed DOT11A100W3 tank car, the P1577/CPC1230 tank car (both with and without a 

jacket), and the Concept 1 tank car. The comparison of the puncture forces for various size 

impactors, provided in Figure 223, shows that the outage volume has very little effect on the 

puncture forces. However, the corresponding comparison of the puncture energies for the various 
177

impactors, provided in Figure 224, shows that the larger outage volumes result in significantly 

increased puncture energies. 

Figure 223. Comparison of calculated puncture forces for 1% and 3% outage.

An example of the corresponding force deflection curves for the 3-, 6-, 9-, and 12-inch square 

impactors for the 1 and 3 percent outage are shown in Figure 225. The comparison shows that 

the force deflection characteristics are similar with the exception that the displacement level, 

where the forces begin to rapidly increase, are significantly larger for the 3 percent outage. This 

can also be seen in the comparison of the tank pressure histories for various impact conditions, 

shown in Figure 226. The larger outage volume allows for larger displacements up to the point 

where the compression of the gasses in the outage volume develops internal pressure levels that 

are significant. 

The relative puncture energy performance for the various tank car designs, summarized in Figure 

224, are mostly consistent between the 1 and 3 percent outage calculations. The one notable 

discrepancy is the Concept 1 design which had clearly the best performance at the 1 percent

outage level but was equivalent to the jacketed P1577/CPC1230 car at the 3 percent outage. This 

illustrates a potential issue associated with multi-layer tank car protection systems. The multiple 

layers have the potential for protection improvements over an equivalent single layer system 

when optimized for a given scenario. However, when impacted in alternative non-optimal 

conditions, the layers can be defeated sequentially, and the performance is degraded below that 

of the single layer. 
178

Figure 224. Comparison of calculated puncture energies for 1% and 3% outage.

Figure 225. Comparison of force-deflection characteristics for 1% and 3% outage.
179

Figure 226. Comparison of calculated tank pressures for analyses with 1% and 3% outage.

5.6.3 Offset Impact Analyses

In addition to the investigation of various impactor sizes and shapes for the general-purpose tank 

cars, a series of analyses were performed to investigate the effects of a vertically offset impact 

point. The analyses and BCs were identical to those used for the 600 lb chlorine tank car 

thoroughly described in Section 4.4.1. The puncture forces and puncture energies for the various 

general purpose tank car designs and offset impact conditions are shown in Figure 227 and 

Figure 228, respectively. It is interesting to note that the 25-inch offset impacts result in 

approximately a 25 percent reduction in the puncture energies for the various general purpose 

tank car designs. This is in contrast to the 60 percent drop in puncture energy for the 25-inch 

offset impact on the 105J600 chlorine tank car. 

Figure 227. Calculated puncture forces for the various vertical offset side impacts.
180

Figure 228. Calculated puncture energies for the various vertical offset side impacts.

Again, in the offset impact analyses, the Concept 1 and 2 designs provide the greatest level of 

protection. An interesting result of these offset impact analyses is that the performance of the 2-

layer Concept 1 design improves relative to the monolithic Concept 2 design as the impact offset 

increases. This suggests that the 2-layer design has potential for increased puncture resistance in 

real-world impact conditions that would include primarily offset and oblique impact conditions. 

5.6.4 Head Impacts of General-Purpose Tank Cars

A suite of impact analyses was performed on various general purpose tank head designs. For 

each design, a set of four impact analyses were performed using different size impactors in offset 

head impacts. A summary of comparative head impact analyses is provided in Table 17. 

The relative head impact puncture energies for the general-purpose tank head impacts are

summarized in Figure 229. In the figure, the puncture energies for each tank head are normalized 

to the corresponding energies for the DOT-111A100W1 tank head. Each point represents the 

calculated puncture energy for the specific tank head normalized by the corresponding puncture 

energy for the DOT-111A100W1 tank head under identical impact conditions. The comparison 

shows the four impact scenarios considered resulted in an average increase in puncture energy of 

23, 79, 80, and 95 percent respectively for the CPC-1230, DOT-111A100W3, CPC-1230J and 

DOT-117A100W tank heads. 
181

Table 17. Summary of the analyses for general purpose tank head impacts.

Head 

Impact 

Analysis

Tank Type Tank 

Head

Jacket 

or Head 

Shield

Impact 

Conditions

Impactor 

Edge 

Radius

Internal 

Pressure

(psi)

Puncture 

Force (lbs)

Puncture 

Energy

(ft-lbs)

R61A DOT-117 0.5938” 

TC128B 

0.500” 

A572-50

15 mph

6”x6” ram 0.50 inch 0 psi 6.765E+05 9.160E+05 

R61B DOT-117 0.5938” 

TC128B 

0.500” 

A572-50

25 mph

12”x12” ram 0.50 inch 0 psi 1.487E+06 2.095E+06 

R61C DOT-117 0.5938” 

TC128B 

0.500” 

A572-50

20 mph

9”x9” ram 0.50 inch 0 psi 1.031E+06 1.690E+06 

R61D DOT-117 0.5938” 

TC128B 

0.500” 

A572-50

10 mph

3”x3” ram 0.50 inch 0 psi 4.132E+05 2.338E+05 

R62A 111A100W3 0.4688” 

A516-70

0.500” 

A572-50

15 mph

6”x6” ram 0.50 inch 0 psi 6.070E+05 8.282E+05 

R62B 111A100W3 0.4688” 

A516-70

0.500” 

A572-50

25 mph

12”x12” ram 0.50 inch 0 psi 1.329E+06 1.744E+06 

R62C 111A100W3 0.4688” 

A516-70

0.500” 

A572-50

20 mph

9”x9” ram 0.50 inch 0 psi 7.232E+05 1.285E+06 

R62D 111A100W3 0.4688” 

A516-70

0.500” 

A572-50

10 mph

3”x3” ram 0.50 inch 0 psi 3.337E+05 3.333E+05 

R63A 111A100W1 0.4688” 

A516-70 N/A 15 mph6”x6” ram 0.50 inch 0 psi 3.865E+05 4.270E+05 

R63B 111A100W1 0.4688” 

A516-70 N/A 25 mph12”x12” ram 0.50 inch 0 psi 7.327E+05 9.490E+05 

R63C 111A100W1 0.4688” 

A516-70 N/A 20 mph9”x9” ram 0.50 inch 0 psi 5.312E+05 7.291E+05 

R63D 111A100W1 0.4688” 

A516-70 N/A 10 mph3”x3” ram 0.50 inch 0 psi 2.224E+05 2.067E+05 

R64A CPC1230J 0.5625” 

TC128B 

0.500” 

A572-50

15 mph

6”x6” ram 0.50 inch 0 psi 6.379E+05 9.100E+05 

R64B CPC1230J 0.5625” 

TC128B 

0.500” 

A572-50

25 mph

12”x12” ram 0.50 inch 0 psi 1.499E+06 1.910E+06 

R64C CPC1230J 0.5625” 

TC128B 

0.500” 

A572-50

20 mph

9”x9” ram 0.50 inch 0 psi 9.846E+05 1.385E+06 

R64D CPC1230J 0.5625” 

TC128B 

0.500” 

A572-50

10 mph

3”x3” ram 0.50 inch 0 psi 3.985E+05 2.391E+05 

R65A CPC1230 0.5625” 

TC128B N/A 15 mph6”x6” ram 0.50 inch 0 psi 5.230E+05 6.100E+05 

R65B CPC1230 0.5625” 

TC128B N/A 25 mph12”x12” ram 0.50 inch 0 psi 9.658E+05 1.297E+06 

R65C CPC1230 0.5625” 

TC128B N/A 20 mph9”x9” ram 0.50 inch 0 psi 7.010E+05 8.360E+05 

R65D CPC1230 0.5625” 

TC128B N/A 10 mph3”x3” ram 0.50 inch 0 psi 2.871E+05 2.030E+05 
182

Figure 229. Normalized impact puncture energy summary for the general-purpose tank 

heads. 

5.6.5 Summary of Analyses for General Purpose Tank Cars 

The analyses discussed in the previous sections of this report show that the various proposed 

designs for general purpose tank cars (improved material selection, increased thickness, and/or 

added jackets) all resulted in increases in the puncture energies compared to the baseline 

111A100W1 tank car. To quantify the magnitude of the improvements, the puncture energy 

obtained from each calculation was normalized by the puncture energy of the 111A100W1 tank 

car in the identical impact scenario. These normalized puncture energies, along with linear fits 

through the data, are summarized in Figure 230. 

The normalized puncture energies show that the baseline P1577/CPC 1230 tank car (without 

jacket) results in an approximately 20 percent increase in puncture energy across the full range of 

impactor sizes. Similarly, the monolithic 5/8-inch-thick TC128B tank car (concept 2) has greater 

than a 50 percent increase in the puncture energy. Adding a jacket to the baseline tank car 

(111A100W3) results in on average approximately a 20 percent increase in puncture energy. 

However, the improvements were less for small impactors and more for large impactors. This 

was similar to the addition of a jacket on the P1577/CPC 1230 tank car where the average 

performance was roughly 40 percent above the 111A100W1 tank car but overall, the 

improvements were greatest for the largest impactors. 
183

Figure 230. Normalized side impact puncture energies for the various general purpose tank 

car designs (1% outage). 

The normalized puncture energies for the analyses of tank cars with the 3 percent outage are 

summarized in Figure 231. The normalization for these analyses is still to the reference 

111A100W1 tank car at 1 percent outage. The trends are again similar where the multi-layer 

systems are seen to perform better for large impactor than small impactors. The biggest 

difference is that the average puncture energy improvements range from approximately 90

percent to more than 130 percent compared to the 111A100W1 tank car at 1 percent outage. 

Figure 231. Normalized side impact puncture energies for the various general purpose tank 

car designs (3% outage). 
184

5.7 DOT Class 113 Cryogenic LNG tank cars

Subsequent the completion of this initial research project in 2013 (Kirkpatrick, 2013), an FRA 

ruling was made that allows transport of LNG in DOT-113C120W9 tank cars. This will likely 

result in increasing shipments of LNG by rail in the future. FRA has an ongoing full-scale test 

program to address the puncture resistance of these tank cars. However, these tests are being 

performed under ideal impact conditions and to date have applied a relatively large 12-inch by 

12-inch impactor. Since these are novel tank designs, there is a risk that under different impact 

conditions (e.g., smaller impactors) the puncture resistance displayed with these tests of the 

DOT-113C120W9 tank cars relative to other designs may not be proportional. It was important 

to identify if this type of vulnerability exists in the design before a significant fleet is put into 

service. As a result, this study was expanded in 2023 to assess the puncture resistance of the 

DOT-113C120W9 under a variety of impactors and impact conditions and compare the relative 

puncture resistance to other designs. 

The DOT-113 cryogenic tank car has many characteristics that are significantly different from 

other tank car designs. It consists of a significantly thicker outer tank (i.e., jacket) that is ring 

stiffened. The space between the inner and outer tanks is larger than for most traditional tank 

cars and is insulated by a vacuum state between the inner and outer tanks. Finally, the inner 

stainless steel tank material at cryogenic temperatures has unique mechanical properties 

compared to traditional tank car steels, as shown in Section 2.5. As a result, the initial effort in 

the DOT-113 puncture resistance study was to validate the model against the full-scale puncture 

test on a DOT-113 tank car with a cryogenic lading. 

5.7.1 Summary of Test Results

A full-scale impact test on the DOT-113 tank car was performed by FRA at the Transportation 

Technology Center (TTC) in Pueblo, CO, on May 14, 2022. The DOT-113 is a double-walled 

cryogenic tank car with a capacity of approximately 34,500 gallons. During the test, an 

approximately 297,000-pound ram car equipped with a 12-inch by 12-inch impactor struck the 

outer shell of the tank car at its mid-height and longitudinally offset 10.8 feet toward the A-end

(FRA, 2022). The measured impact speed was 22.1 mph which corresponds to an impact energy 

of 4.8 million foot-pounds. The tank car and ram position prior to impact is shown in Figure 232. 

The measured force-displacement behavior for the ram car during the test is shown in Figure 

233. The maximum force of approximately 1.7 million pounds occurs immediately prior to the 

tank puncture corresponding to an impactor indentation of approximately 60 inches. The tank car 

absorbed 4.3 million foot-pounds of energy prior to puncture. After puncturing the inner tank, 

the impactor continued moving at a speed of approximately 7 mph before coming to rest with the 

head of the impactor lodged inside the inner tank. 
185

Figure 232. Pre-impact configuration of the DOT-113 tank car and ram for Test 13 (FRA, 

2022). 

Figure 233. Measured ram car force-displacement and energy dissipation for Test 13. 

The test plan was developed with an objective of filling the tank car to approximately 97 percent 

by volume with liquid nitrogen (LN2). The outage volume contained pressurized gaseous 

nitrogen (GN2) at a pressure of 21 psig immediately prior to the test (FRA, 2022). The measured 

pressure history inside the tank during the test is shown in Figure 234. During the initial phase of 

the impact, the tank is compressed, and the internal pressure begins to rise. After approximately 

100 ms the pressure reaches a point at which it stabilizes at approximately 65 psig. It is believed 

that this pressure level is maintained as subsequent compression results in GN2 condensing to 
186

LN2 and the outage volume is reduced. After approximately 180 ms the pressure begins to rise 

again as the tank nears a shell-full condition. A peak pressure on the order of 150 psi is achieved 

immediately prior to tank puncture. 

Figure 234. Measured internal tank pressures for Test 13. 

5.7.2 Model Validation

The model for the test 13 impact analyses is shown in Figure 235. The model includes the ram 

car, DOT-113 test car resting on skids, and the impact wall. The model includes 3.9 million 

nodes with 1.24 million 4-node shell elements and 2.36 million 8-node solid hexahedron (i.e., 

brick) elements. A significant portion of the model is a highly refined mesh in the impact zone, 

shown in Figure 236, with solid elements with a characteristic size in the rupture zone of 

approximately 1 mm. 

Figure 235. Model of the DOT-113 tank and Test 13 impact configuration. 
187

Figure 236. Mesh of the impact zone in the DOT-113 tank car model. 

In the analyses, a control volume was established for the tank and the change in volume was used 

to calculate a corresponding change in pressure (using an airbag algorithm in LS-DYNA). Posttest analyses of the tank indicated that the outage volume was likely closer to 4 percent than the 

target 3 percent level. The absolute pressure-volume relationship used for the analysis of the test 

is shown in Figure 237. The figure compares the behavior for an ideal gas constant temperature 

compression with the modified behavior used that includes a constant pressure region during 

condensation of the GN2 to LN2. In the modified curve, the pressure reaches a plateau at 

approximately 80 psi starting at an outage volume of 1.85 percent (relative volume of 0.9785) 

and remains at that pressure until the outage is reduced to approximately 0.5 percent (relative 

volume of 0.965) at which point the pressure again continues to increase approaching the shell 

full condition (relative volume of 0.96). 

Figure 237. Tank pressure volume relationships used for analysis of Test 13. 
188

The calculated tank impact response just prior to tank rupture (200 ms after impact) is shown in 

Figure 238. At this time, the ram has indented the tank by 57 inches and the impact force is 

above 1.5 million lbs. The corresponding calculated force-displacement and energy absorption 

plots are compared to the measured Test 13 response in Figure 239. The comparison shows a 

sufficiently good correlation between the force-deflection response and the force and 

displacement levels at the tank puncture to validate the modeling methodology for assessing the 

puncture resistance of the DOT-113 tank car. 

Figure 238. Calculated tank impact response just prior to tank rupture. 

Figure 239. Comparison of the calculated and measured force-displacement behavior in 

Test 13. 

The additional comparison of the measured and calculated tank pressure histories for Test 13 are 

shown in Figure 240. The agreement in the characteristics of the pressure histories indicates that 
189

the modified pressure curve with a phase change occurring at approximately 80 psi is the likely 

behavior for the LN2 lading in this test. 

Figure 240. Calculated tank impact response just prior to tank rupture. 

5.7.3 DOT Class 113 LNG Tank Model

The full model of the DOT-113 tank car used for the model validation efforts described above 

was not considered to be appropriate for the subsequent assessment of the relative puncture 

resistance. First, the tank car design had proprietary design features that do not allow for any 

symmetry planes to be incorporated. In addition, it includes features such as the detailed sill and 

bolster models which do not have a significant effect on the puncture response. As a result, a 

simplified generic DOT113 tank model was developed for the following assessments of the 

relative puncture resistance. 

The generic DOT113 Tank model developed for the tank puncture resistance assessment is 

shown in Figure 241. The tank model is again a double tank construction with a stiffened outer 

tank and cryogenic inner tank with vacuum insulation between tanks. The tank diameters and 

thicknesses were the same as those of the Test 13 DOT-113 tank car. However, the geometry is 

simplified such that the model includes both vertical and longitudinal symmetry planes. In 

addition, the material model for the inner tank was swapped to that of the A240 304 stainless 

steel at LNG cryogenic temperature (-260F, 110K). 

The other significant modification required for analysis of a DOT-113 tank car for LNG service 

is the definition of appropriate outage volume and the pressure-volume relationship during 

impact. Multiple sources were used to develop a nominal pressure-volume relationship for a 

DOT-113 tank car transporting LNG. From the PHMSA LNG by rail final rule (PHMSA, 2020), 

the loading pressure when offered for transportation must be a maximum of 15 psi. The 

corresponding maximum start to discharge pressure is 75 psi (safety relief valve setting). The 

corresponding outages for these pressures are approximately 9 percent at loading and 2 percent at 

the start to discharge condition. 
190

(a) Quarter-symmetry model of tank, ram, and reaction wall

(b) Mesh resolution of the outer tank impact patch

Figure 241. Model of a generic DOT-113 tank for analysis of puncture resistance.

Expected pressure conditions during shipment were provided in an example by the National 

Academies (National Academies of Sciences, Engineering, and Medicine, 2022): “These 

materials must be shipped in tank cars designed to minimize heat input so as to limit pressure 

rise to 3 pounds per square inch gauge (psig) (1.2 bar) per day. For example, ethylene is 
191

authorized to be offered for transportation at 20 psig and a corresponding temperature of −125°F 

(−87°C). Because the lading will continue to warm until delivery and the daily pressure rise of a 

DOT-113 tank car is 0.5 to 0.75 psig (1.05 to 1.07 bar), the temperature and pressure at the end 

of a 10-day trip is expected to be about −117°F (–83°C) and 27.5 psig (2.9 bar).” If we apply 

upper bound LNG transport conditions of 15 psi loading pressure and a maximum increase of 3 

psi per day that would still limit the pressure at arrival to the destination to 45 psi for a 10-day 

transit. 

Since the risk of a derailment/impact is uniform over the transit, the average condition at impact 

would be the midpoint between the loading condition and the arrival condition. However, a 

lower outage volume and higher initial pressure would result in a more conservative estimate of 

the puncture resistance. As a result, we selected a 30-psig initial pressure and a corresponding 

outage of approximately 7.5 percent for the nominal condition in the puncture resistance 

assessment. 

The final consideration for the LNG pressure volume behaviors in impact is the shape of the 

pressure-volume curve. The two possibilities are an ideal gas pressure-volume curve, like the 

behaviors used for other hazmat commodities [e.g., (Kirkpatrick, 2009a), (2013)] or a curve that 

allows for a gas-to-liquid phase change as seen in the Test 13 LN2 response (Figure 237). A 

comparison of these two possible behaviors is shown in Figure 242. 

Figure 242. Tank pressure volume relationships used for puncture analysis of the DOT-113 

LNG tank car.

To support the selection of a pressure-volume relationship to use on the DOT-113 puncture 

resistance assessment, a set of preliminary analyses was performed using both behaviors. The 

puncture behaviors for both a 30-mph impact with the 12x12-inch impactor and 20 mph impact 

with the 6x6-inch impactor are shown in Figure 243 and Figure 244, respectively. During the 

initial impact response, the pressure curves are identical, so the resulting impact response is 

identical. For the 12x12-inch impactor the response diverges after approximately 45 inches of 

ram displacement. The pressure behavior with phase change allows for somewhat reduced forces 

during the subsequent impact but a corresponding increase of displacement to puncture of 2.6 
192

inches. As a result, the analysis with the phase change dissipates 0.5 percent more of the impact 

energy at puncture. 

Figure 243. Calculated and measured force-displacement behaviors for the Test 13 impact 

condition. 

For the 6x6-inch impactor the response is identical until immediately preceding the puncture 

response. This is because the tank only reaches a compression of the volume to reach the gas-toliquid transition pressure at the point near the puncture condition. As a result, the analysis with 

the phase change dissipates 1.2 percent more of the impact energy at puncture. 

Figure 244. Calculated and measured force-displacement behaviors for the Test 13 impact 

condition. 
193

Preliminary Analysis of Validation Test Conditions

Prior to performing the full assessment of the baseline DOT-113 tank car design under a range of 

impact conditions, a pair of analyses were performed with the simplified generic DOT-113 tank 

impact model using the approximate Test 13 impact conditions. In these analyses, the pressure 

volume relationships for the LN2 in Test 13, shown previously in Figure 237, were applied. To 

evaluate the effects of the gas-to-liquid phase change, analyses were performed both with the 

ideal gas pressure behavior as well as the modified behavior including the phase change effect. 

In addition, these analyses maintained the constitutive behavior of the inner tank for the A240 

304 stainless steel at the colder LN2 cryogenic temperature (-321F, 77K), described in Section 

2.5.2. 

The calculated response for the Test 13 impact condition with the generic DOT-113 model is 

shown in Figure 245. In the figure, the model has been reflected about the vertical plane to 

present a cross-sectional half model view. The deformed shape, shown in Figure 245(b) is at the 

point of inner tank puncture and the ram is seen to have fully penetrated the outer tank. In this 

analysis the ram displacement (i.e., tank indentation) is slightly more than 60 inches when 

puncture occurs. 

(a) Cross section of the tank, ram, and reaction wall model

(b) Tank deformation at puncture

Figure 245. Analysis of the generic DOT-113 tank in the Test 13 impact conditions.
194

The comparison of the calculated force-deflection behaviors with the generic DOT-113 tank 

geometry are compared to the measured Test 13 behavior in Figure 246. As expected, the 

analyses provide an identical response for the initial 35 inches of ram displacement (approx. 0.1 

s) where the pressure curves are identical. Some differences are observed in the subsequent 

impact response resulting from internal pressure differences. Again, the phase change allows for 

lower forces after the initiation of phase change stabilizes internal pressure and a slightly larger 

displacements prior to reaching the puncture condition. As a result, puncture energy is increased 

by 1.6 percent by including the phase change response.

Figure 246. Calculated and measured force-displacement behaviors for the Test 13 impact 

condition. 

5.7.4 Baseline DOT Class 113 LNG Tank Analyses

The generic DOT-113 tank car model was applied to analyze puncture conditions for the 

standard suite of side impact conditions. The baseline analyses normal impacts include the 3x3, 

6x6, 9x9, 12x12, and 3x12 rectangular impactors as well as the 5.73-, 7.64-, 9.55-, 11.46-, and 

13.37-inch diameter round impactors. The calculated impact force-deflection and puncture 

energy dissipation curves for these impacts on the DOT-113C120W9 tank car are summarized in 

Table 18 and shown in Figure 247. 

As a baseline comparison of the puncture resistance for the DOT-113C120W9 LNG tank car, the 

puncture energies for each impact scenario were normalized against the corresponding puncture 

energies for the DOT-105J500W chlorine tank car. These normalized tank car puncture energies 

are then plotted against those of the other TIH pressure tank car designs (previously summarized 

in Section 5.5) in Figure 248. The average puncture energy for the DOT-113C120W9 tank car is 

126 percent higher than the DOT-105J500W chlorine tank car. In addition, the average puncture 

energy for the DOT-113C120W9 tank car is higher than those of all the TIH pressure tank car 

designs that have been analyzed. 
195

Table 18. Summary of the baseline side impact analyses on the DOT-113C120W9 tank car

Calculation Tank Type Tank Shell Shell 

Jacket 

Impact 

Conditions

Internal 

Pressure

(psi)

Puncture 

Force (lbs)

Puncture 

Energy

(ft-lbs)

RL3A DOT-113 0.29 in

SS304L 

0.5625 in

TC128B 

20 mph

6”x6” ram 30 psi 9.172E+05 3.098E+06 

RL3B DOT-113 0.29 in

SS304L 

0.5625 in

TC128B 

30 mph

12”x12” ram 30 psi 2.020E+06 6.278E+06 

RL3C DOT-113 0.29 in

SS304L 

0.5625 in

TC128B 

25 mph

9”x9” ram 30 psi 1.461E+06 4.651E+06 

RL3D DOT-113 0.29 in

SS304L 

0.5625 in

TC128B 

15 mph

3”x3” ram 30 psi 4.857E+05 8.629E+05 

RL3E DOT-113 0.29 in

SS304L 

0.5625 in

TC128B 

15 mph

3”x6” ram 30 psi 6.439E+05 1.919E+06 

RL3F DOT-113 0.29 in

SS304L 

0.5625 in

TC128B 

25 mph

3”x12” ram 30 psi 1.184E+06 3.449E+06 

RL3G DOT-113 0.29 in

SS304L 

0.5625 in

TC128B 

20 mph

5.73 in. dia. 30 psi 8.416E+05 1.957E+06 

RL3H DOT-113 0.29 in

SS304L 

0.5625 in

TC128B 

20 mph

7.64 in. dia. 30 psi 1.046E+06 3.214E+06 

RL3I DOT-113 0.29 in

SS304L 

0.5625 in

TC128B 

25 mph

9.55 in. dia. 30 psi 1.296E+06 4.193E+06 

RL3J DOT-113 0.29 in

SS304L 

0.5625 in

TC128B 

30 mph

11.46 in. dia. 30 psi 1.590E+06 5.492E+06 

RL3K DOT-113 0.29 in

SS304L 

0.5625 in

TC128B 

35 mph

13.37 in. dia. 30 psi 1.618E+06 6.190E+06 

To evaluate the factors that lead to the high puncture resistance of the DOT-113C120W9 tank 

car compared to other pressure tank car designs, the calculated force-deflection behaviors are 

compared to those of the DOT-105J500 EO and DOT-105J600 CL tank cars for the 6- and 12-

inch square impactors in Figure 249 and Figure 250, respectively. The comparison shows that the 

puncture forces of the pressure tank car designs are equivalent or higher to that of the DOT-113 

tank car. However, the DOT-113 tank car has a significantly more compliant impact response 

with higher displacement, and thus higher impact energy dissipation, prior to puncture. 
196

Figure 247. Force-deflection response and energy absorption for the DOT-113 tank in 

normal side impacts. 

Figure 248. Comparison of the DOT-113 LNG tank car to various TIH commodity 

pressure tank car designs. 
197

Figure 249. Comparison of the DOT-113 tank with other pressure tanks (6x6 impactor). 

Another relevant comparison for the DOT-113C120W9 LNG tank car is to compare to the 

general-purpose tank cars that have traditionally been used to carry other flammable 

commodities (e.g., crude oil and ethanol). In this comparison, the DOT-113C120W9 tank car 

puncture energies for each impact scenario were normalized against the corresponding puncture 

energies for the DOT-111A100W1 tank car. These normalized tank car puncture energies are 

then plotted against those of the other general purpose tank car designs (previously summarized 

in Section 5.6.5) in Figure 251. The average puncture energy for the DOT-113C120W9 tank car 

is 8.46 times higher than that of the DOT-111A100W1 tank car. In addition, the average 

puncture energy for the DOT-113C120W9 tank car is much higher than those of all the generalpurpose tank car designs that have been analyzed. 

Figure 250. Comparison of the DOT-113 tank with other pressure tanks (12x12 impactor). 
198

Figure 251. Comparison of the DOT-113 tank puncture resistance to non-pressure general 

purpose tank designs.

5.7.5 Modified DOT Class 113 LNG Tank Analyses

Although the puncture resistance of the baseline DOT-113 LNG tank design was quite high, 

additional analyses were performed to evaluate potential DOT-113 enhancements designed to 

increase the puncture resistance. In this section, we evaluate design variations with increased 

inner and outer tank thicknesses to assess as optimum design for increased puncture resistance.

Preliminary Analyses to Select Design Modification

Preliminary analyses were performed with both small (6x6-inch) and large (12x12-inch) 

impactor on proposed designs with additional thickness applied independently to the inner and 

outer shells. Based on the results of these preliminary analyses, a modified design was selected, 

and a full puncture assessment performed. 

In these preliminary comparisons, the inner and outer tank shells were separately increased in 

thickness by an additional 1/8-inch. The calculated force-deflection and impact energy 

dissipation curves for these preliminary proposed modifications are compared to the baseline 

DOT-113 tank design for the 6- and 12-inch square impactors in Figure 252 and Figure 253, 

respectively. For both scenarios, the concept with the increased inner tank shell thickness results 

in the greatest increase in puncture resistance. Note that due to the smaller diameter of the inner 

tank, this modification would also result in a smaller increase in the tank light weight. 
199

Figure 252. Preliminary mitigation analyses for the DOT-113 tank car (6x6 impactor). 

Figure 253. Preliminary mitigation analyses for the DOT-113 tank car (12x12 impactor). 

Analyses of the Modified Design 

Based on the preliminary analyses of the design modification, researchers selected the one with 

an increased thickness of the internal tank shell. However, the appropriate magnitude of the 

increase in the tank shell still needed to be determined. The final decision was based on a 

consideration of the AAR Specification M-1004 which covers LNG fuel tenders. By increasing 

the internal tank thickness to 0.50 inch, the tank design would be equivalent to an LNG tender 

tank that is M-1004 compliant. A summary of the tank shell parameters for this tank compared to 

the baseline DOT-113 tank is provided in Table 19. 
200

Table 19. Summary of the LNG tank car design parameters.

Tank Designation Tank Shell Tank Jacket Combined Thickness 

Baseline DOT-113C120W9 0.29-inch SS304L 0.5625-inch TC128B 0.8525 inch

M-1004 Compliant DOT-113 0.50-inch SS304L 0.5625-inch TC128B 1.0625 inch

The modified M-1004 tank was similarly evaluated using the same suite of side impact 

conditions used for the baseline DOT-113 LNG tank car. The calculated puncture energies for 

the M-1004 LNG tank normalized to those of the baseline DOT-113 LNG tank are shown in 

Figure 254. The M-1004 compliant tank design has on average a 44 percent increase in the 

puncture energy. The puncture resistance improvements are also seen to be higher for the small 

and medium size impactors. 

Figure 254. Comparison of the M-1004 compliant LNG tank car to the baseline DOT-113 

tank car design. 

A comparison of the puncture resistance for the M-1004 compliant LNG tank car to TIH 

pressure tank cars is obtained through normalization against the corresponding puncture energies 

for the DOT-105J500W chlorine tank car. These normalized tank car puncture energies are then 

plotted against those of the baseline DOT-113 tank car and other TIH pressure tank car designs 

(previously summarized in Section 5.5) in Figure 255. The average puncture energy for the 

DOT-113C120W9 tank car is approximately 3 times that of the DOT-105J500W chlorine tank 

car. In addition, the average puncture energy for the M-1004 compliant LNG tank car is 

significantly higher than those of all the TIH pressure tank car designs that have been analyzed. 
201

Figure 255. Comparison of the M-1004 compliant LNG tank car to various TIH commodity 

pressure tank car designs. 

5.7.6 Head Impacts of DOT Class 113 LNG Tank Cars

A suite of impact analyses was performed on both the baseline DOT-113 and the modified M1004 compliant LNG tank head designs. A set of four impact analyses were performed for each 

design using different size impactors in offset head impacts. A summary of comparative head 

impact analyses is provided in Table 20. The calculated force-deflection behaviors and integrated 

puncture energy curves for the baseline and modified DOT-113 tank heads is shown in Figure 

256 and Figure 257, respectively. 

Table 20. Summary of the impact analyses for baseline DOT-113 head impacts. 

Head 

Impact 

Calculation

Tank 

Type

Tank 

Head

Jacket 

or Head 

Shield

Impact 

Conditions

Impactor 

Edge 

Radius

Internal 

Pressure

(psi)

Puncture 

Force (lbs)

Puncture 

Energy

(ft-lbs)

R71A DOT-113 

LNG

0.300” 

SS-304

0.5625” 

TC128B

15 mph

6”x6” ram 0.50 inch 30 psi 9.234E+05 2.181E+06 

R71B DOT-113 

LNG

0.300” 

SS-304

0.5625” 

TC128B

25 mph

12”x12” ram 0.50 inch 30 psi 1.891E+06 3.917E+06 

R71C DOT-113 

LNG

0.300” 

SS-304

0.5625” 

TC128B

20 mph

9”x9” ram 0.50 inch 30 psi 1.139E+06 2.685E+06 

R71D DOT-113 

LNG

0.300” 

SS-304

0.5625” 

TC128B

10 mph

3”x3” ram 0.50 inch 30 psi 6.258E+05 9.430E+05 

R72A M-1004 

LNG

0.510” 

SS-304

0.5625” 

TC128B

15 mph

6”x6” ram 0.50 inch 30 psi 1.453E+06 2.471E+06 

R72B M-1004 

LNG

0.510” 

SS-304

0.5625” 

TC128B 

25 mph

12”x12” ram 0.50 inch 30 psi 2.069E+06 4.865E+06 

R72C M-1004 

LNG

0.510” 

SS-304

0.5625” 

TC128B

20 mph

9”x9” ram 0.50 inch 30 psi 1.526E+06 3.265E+06 

R72D M-1004 

LNG

0.510” 

SS-304

0.5625” 

TC128B

10 mph

3”x3” ram 0.50 inch 30 psi 8.335E+05 9.383E+05 
202

Figure 256. Calculated force-deflection behaviors for DOT-113 tank head impacts.

Figure 257. Calculated force-deflection behaviors for the modified DOT-113 tank head

impacts.

The relative head impact puncture energies of the baseline DOT-113 normalized to the 

corresponding energies of the modified M-1004 compliant DOT-113 tank head is shown in 

Figure 258. Each point on Figure 258 represents the calculated puncture energy for the modified 

DOT-113 tank head normalized by the corresponding puncture energy for the baseline DOT-113 

tank head for the same impactor. The individual scenarios result in a range of normalized 

puncture energies from a minimum of 1.22 for the 9-inch impactor to a maximum of 1.79 for the 

smallest 3-inch impactor (22-79 percent higher puncture energies). The four impact scenarios 

considered results in an average increase in puncture energy of 45 percent for the modified DOT-
203

113 over the baseline DOT-113 LNG tank head. This magnitude is consistent with the 44 percent 

average impact energy increase obtained for the side impacts. 

Figure 258. Normalized impact puncture energy summary for the DOT-113 tank heads.

The relative head impact puncture energies of the DOT-113 LNG tank heads normalized to the 

corresponding energies of the legacy 105J500 chlorine tank head are shown in Figure 259. The 

four impact scenarios considered result in an average increase in puncture energy of 56 percent

and 127 percent for the baseline and modified DOT-113 tank heads, respectively, relative to the 

500 lb chlorine tank head. The puncture resistance for both designs is also significantly greater 

than those of the other pressure tank car designs that were evaluated, as shown in Figure 259. 

Figure 259. Normalized puncture energy summary for the baseline DOT-113 tank heads.
204

6. Analytical Models for Tank Car Impacts

6.1 Introduction

The detailed FE impact analyses and BW failure have been extensively applied to assess various 

tank impact conditions as described in Sections 3 through 5 of this report. The FE modeling 

approach is very useful for understanding the mechanics of tank impacts and punctures. 

However, at times, a simplified analysis methodology or impact algorithm is useful for the 

assessment of various factors on tank impact safety. As a result, other researchers have 

developed similar analytical approaches for tank impacts [e.g., (Jeong, Tang, & Pearlman, 

2001a), (2001b), (Jeong, Tang, Yu, & Pearlman, 2006)]. However, these have typically been 

developed and applied to very limited sets of impact conditions. In this chapter, we describe the 

development of tank impact algorithms. 

When assessing appropriate analysis methodologies, we examined the response characteristics of 

both head and side impacts. We found that the behaviors for these two impact conditions are 

sufficiently unique that different analysis methodologies were appropriate for the head and side 

impacts. These will be described in separate sections of this chapter. 

6.2 Head Impact Analyses

The head impact response has several characteristics that influenced the methodology applied for 

the simplified impact algorithm. The tank head is a stiffer structure under impact and the impact 

behavior for a constrained head is relatively independent of the impact speed (minimal dynamic 

effects – see Section 3.4). The most common head impact scenario is with the motions and 

orientations of the impacted and impacting cars nearly aligned with the original direction of 

travel. As a result, the motions can be assumed to be primarily one dimensional. In addition, the 

effects of the lading model assumptions are much more significant for head impacts on 

unconstrained tanks. As a result, a unique analytical methodology was used to develop an 

algorithm for head impacts. 

6.2.1 Head Impact Analysis Algorithm 

The initial methodology for the head impact response algorithm was developed and validated 

against the analyses of head impacts with different constraint conditions described previously in 

Section 1.1.1. The constraint effects in head impacts are bounded by analyses of the fully 

constrained tank head and an unconstrained tank. The unconstrained tank model includes the 

entire tank which is free to translate. To bounds the lading effects on the unconstrained tank 

analyses were performed where, in the first analyses, none of the weight of the lading was added 

to the tank, and in the second analysis, all the lading mass was smeared into the tank. 

The force-deflection curves for initial set of impact analyses used in the assessment of the 1D 

impact algorithm are shown in Figure 260. The analyses are for an 18-mph impact of the 9.55-

inch-diameter round impactor. The three analyses are the constrained tank head impact and the 

two unconstrained tank models at the different tank weights. 

A simple 1D algorithm was developed for the head impact tank motions with the different 

constraint conditions. The algorithm uses a known force-deflection curve of the fully constrained 

tank head as a characteristic property of the tank structure. The forces are then used to update the 

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respectively are compared to the detailed FE analyses in Figure 261. The comparison shows that 

the simple approach of an uncoupled force versus dent depth interaction and tank motions 

describe most of the impact behavior. The largest deficiency of the 1D algorithm is that the 

nonlinear unloading behavior was not included in the analyses. In the detailed FEA a residual 

dent is maintained in the unloading process as the tank separates from the impactor. In the 

preliminary development of the algorithm the dent displacement unloads along the original 

loading curve. 

Figure 261. Comparison of the 1D model and FEA predictions for tank impact forces 

(18 mph impacts). 

A modification was made to the model to include the unloading effects. The approach uses a 

linear unloading modulus when the relative motions between the tank and the ram are negative. 

To estimate the unloading modulus, the plots of force versus relative displacement for the 18 

mph impacts of the loaded and empty tanks are compared in Figure 262. The comparison shows 

that a linear unloading behavior is a reasonable approximation and the unloading modulus of 

approximately 2 million lbs/in is a good average value for the 600 lb tank head. 

Using the modified model with unloading, the force-deflection behaviors predicted by the simple 

1D algorithm for the two unconstrained tank impacts with the empty and full tank weights are 

compared to the detailed FE analyses in Figure 263. The comparison shows that the simple 

algorithm accurately reproduces the force versus dent depth interaction and tank motions for the 

full impact and unloading behavior. 
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Figure 262. Comparison of the FEA analyses with unloading behaviors. 

Figure 263. Comparison of the 1D model and FEA predictions with unloading 

(18 mph impacts). 

To confirm the performance of the algorithm, we applied it to a similar set of analyses using the 

coupler impactor model and an impact speed of 25 mph. The force deflection curves for these 

analyses are compared in Figure 264. The comparison of the detailed FEA and the simplified 1D 

head impact algorithm is shown in Figure 265. The comparison shows again that the simplified 

1D algorithm does a good job of predicting the force-deflection curves for the head impacts on 

the tank. 
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Figure 264. The effects of BC restraint on head impact response 

(25 mph coupler impacts). 

Figure 265. Comparison of the 1D model and FEA predictions with unloading 

(25 mph coupler impacts). 

One of the complexities of this approach is that the detailed force-deflection curve for a fixed 

tank head was obtained from a detailed FEA and applied in a tabular lookup to obtain the 

interaction forces. An alternative approach is to use a simplified linear stiffness for the forcedeflection behavior of the tank head. We can approximate the indentation stiffness of the 600 lb 

chlorine tank head and head shield at 80,000 lb/in. A comparison of this constant stiffness 

approximation to the fixed head force-deflection curves is shown in Figure 266. Using this 

constant stiffness value in the 1D algorithm we can recalculate the force-deflection behaviors for 

the empty and full tanks for the 18 and 25 mph impacts. The comparison of the constant stiffness 

1D algorithm approximation to the detailed FEA results is shown in Figure 267. Again, the 
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overall agreement is quite good. The largest discrepancies are for the late time impacts on the 

loaded tanks where the force reduction from the head shield damage is not captured by the 

constant stiffness approximation. 

Figure 266. Comparison of the FEA and constant stiffness approximation. 

Figure 267. Comparison of the 1D model and FEA predictions with unloading 

(fixed head stiffness - 18 and 25 mph impacts). 

6.3 Side Impact Analyses 

The side impact response has several characteristics that influenced the methodology applied for 

the simplified impact algorithm. The tank is a more compliant structure under side impacts and 

the impact behavior is not independent of the impact speed (dynamic effects – see Section 3.4). 

The impact scenarios under side impacts are also typically occurring in large scale lateral 
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buckling behaviors of a derailment where the motions of the various cars are chaotic. As a result, 

the side impacts will include a greater range of variability in impact location and orientation. As 

a result, the motions will be at least two dimensional. As a result, a unique analytical 

methodology was used to develop an algorithm for side impacts. 

6.3.1 Supporting FE Tank Analyses

In the previous sections of the report, many of the possible behaviors of tank cars in various side 

impact conditions have been analyzed. This information will be used to assist in the development 

and validation of the side impact model. However, there are other aspects of the tank response 

that are difficult to extract from the complex impact analyses. As a result, a series of idealized 

tank side loading analyses were performed to address some of the physics of tank behaviors. 

An example of the type of additional analysis performed to assist the development of the 

analytical model is an analysis of the effects of different BCs. A series of analyses were 

previously performed to assess different tank constraint conditions as described in Section 4.3.1

of this report. Initially, a series of side impact analyses were performed where the impacted tank 

was placed against a wall, against another tank, and free to translate. The effects of the BCs 

could be detected but under the dynamic impact conditions the effects are seen only at late times 

in the response. 

To more clearly evaluate the effects of the boundary constraints, idealized impact scenarios were 

analyzed where the tank was loaded at slow rates and under symmetrically conditions between 

two rams or two walls. Under these loading conditions, the tank has relatively linear force 

deflection curves and both fail at roughly equivalent puncture forces, as shown in Figure 268. 

Figure 268. The effects of constraint BCs on the side impact response.

The quasistatic loading with a 9.55-in.-diameter rams of a tank against the wall fails at a force of 

approximately 1.5 million lbs and a ram displacement of approximately 40 inches. The 

symmetric loading between two 9.55-in.-diameter rams fails at a similar load level and a 

corresponding ram displacement of approximately 30 inches. However, the symmetric condition 

assumes that the tank is between two moving rams. Thus, the total compaction of the tank 
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between the two ram faces is approximately 60 inches. The calculated force-deflection for the 

symmetric wall loading develops a 1.5 million lb reaction load over a displacement of 

approximately 10 inches (after the initial 4-inch standoff distance of the jacket from the tank is 

crushed). 

The significant difference in the compliance of the tank against either an impactor or the reaction 

wall is a result of the load application over a much larger area with the wall. This suggests that 

the size of the wall would have a significant effect on the wall reaction forces and tank 

deformations against the wall. To investigate this effect, a series of analyses were performed 

where the tank is quasistatically compressed between walls of different sizes (symmetric loading 

analyses). 

In the initial series of analyses, the length of the wall was varied. The height of the wall is 6 feet 

and centered on the tank height. This dimension is sufficiently large that it exceeded the height 

of the contact patch of the tank and jacket for all the analyses. The baseline width of the wall was 

25 feet to match the width of the impact wall at the transportation Technology Center Inc. 

(TTCI) test facilities where the NGRTC tests were performed (Kirkpatrick, 2009a). Additional 

widths analyzed included 1, 4, 8, 16, and 32 feet. This ranges from a very narrow width that will 

behave as if the tank were resting against a structural column to a wide width that extends nearly 

the full length of the tank shell. The models for the 1-foot and 32-foot wall length analyses are 

shown in Figure 269. 

(a) 32-foot wall length

(b) 1-foot wall length

Figure 269. Comparison of models used to investigate reaction wall size effects.
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The comparison of the force-deflection curves for the analyses with the different wall lengths is 

shown in Figure 270. The comparison shows that the wall length has a significant influence on 

the stiffness of the reaction forces. This effect is not too surprising since a longer section of the 

tank cylinder is being compressed with the longer wall. To quantify the effect, we plot the 

approximate steady state stiffness of the tank compression against the wall width as shown in 

Figure 271. The comparison shows a relatively linear increase in the tank stiffness as the width 

of the wall is increased. The non-zero intercept of the ordinate in Figure 271 is probably an 

indication of the magnitude of the edge effect for the tank denting outside the direct load 

application region against the wall. 

Figure 270. The effects of constraint wall width on the reaction loads.

Figure 271. The effects of wall width on the tank compression stiffness.
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These effects of the reaction wall width can be seen in an impact analysis where the tank 

dynamics and wall interaction are significant. A series of analyses were performed for a 15-mph 

impact of the 9.55-in-diameter round impactor. This impact condition is below the puncture 

threshold for the 105J600W chlorine tank car. The three BCs analyzed were a free tank (no wall) 

and a tank against the 1-foot-wide and 25-foot-wide reaction walls. The force-displacement 

curves for these three analyses are shown in Figure 272. The initial loading behaviors for all 

three analyses are identical but the tank dynamics (unloading and reloading) at the large 

displacement levels are significantly different. 

Figure 272. The effects of wall width on the tank impact behavior. 

The effects of the wall interaction can be seen more clearly in the force-time histories for the 

three impact analyses, shown in Figure 273. With no wall, the tank loads up against the impactor 

over the initial 150 ms followed by an unloading over the next 80 ms as the tank is pushed away 

from the impactor. With the 25-foot-wide wall, the motions of the tank interact with the stiff wall 

to resist the tank motions and the rebound off the wall and reloading process starts at a time of 

approximately 180 ms (approximately halfway through the unloading). The reloading behavior 

reaches a peak force that is approximately 10-15 percent higher than the peak force in the initial 

loading. 

The impact with the 1-foot-wide reaction wall allows for a much more compliant behavior of the 

tank against the wall. As a result, the wall reaction forces develop more slowly, and the tank 

rebound off the wall and reloading process starts at a time of approximately 250 ms after the 

initial impact force has completely unloaded. As a result of the longer overall impact duration, 

there is less residual impact energy and the peak force in the reloading behavior is approximately 

5 percent lower than the peak force in the initial loading. 
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Figure 273. The effects of wall width on the impact force histories. 

An additional series of analyses was performed to investigate the effects of the wall height. The 

32-foot-wide wall was used for these analyses. The 6-foot height is sufficiently large that it 

exceeded the height of the contact patch of the tank and jacket for all the analyses. As a result, 

smaller heights of 1, 2, and 4 feet were also investigated. The comparison of the force-deflection 

curves for the analyses with the different wall heights is shown in Figure 274. The comparison 

shows that the wall height has a small influence on the stiffness of the reaction forces. This 

suggests that the shape of the tank deformations against the wall do not vary significantly with 

much smaller wall heights. A comparison of the 1-foot and 6-foot wall height deformations is 

provided in Figure 275. There are differences in the deformations of the outer jacket, but the 

deformations of the commodity tanks are very similar. 

Figure 274. The effects of constraint wall height on the reaction loads.
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(a) 1-foot wall height (b) 1-foot wall height

Figure 275. Comparison of Tank Deformations with different wall heights.

The baseline side impact algorithm development was performed for the 600 lb chlorine tank car 

(105J600W) at a 100-psi internal pressure. However, for the algorithm to have greater utility, it 

needs to be applicable to other tank car designs and pressure levels. One approach to extending 

the analysis to other tank cars or pressure conditions is to develop scale factors for the system 

stiffness base on the tank design parameters. To assess these potential scale factors, a series of 

quasistatic compression analyses were performed on a tank where the thickness, radius, and 

pressure were varied independently. 

The analyses were performed for the quasistatic symmetric compression loading of a tank 

between two 25-foot-wide walls. In the initial series of analyses, the diameter of the tank and the 

initial internal pressure were held constant, and the thickness of the tank shell was varied. The 

thickness variations evaluated were 1/2, 2/3, and 5/6 of the original 600 lb tank shell thickness. 

The calculated force deflection curves for these different thickness tanks are shown in Figure 

276. The thickness has a moderate influence on the tank stiffness under the side loading. 

Figure 276. The effects of tank thickness on quasistatic compression loads. 
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To quantify the effect, we determined the relative stiffness of the various tanks between 8 and 12 

inches of displacement. This is a relatively linear portion of the response after the initial jacket 

compaction is complete and before the variable pressure effects become large. A plot of this 

effective tank stiffness against the tank wall thickness is shown in Figure 277 A fit shows a 

relatively linear increase in the tank stiffness with changes to the tank shell thickness. 

Figure 277. The effects of tank thickness on quasistatic compression stiffness. 

In the second series of analyses, the tank shell thickness was fixed (0.981-in-thick TC128B) and 

the initial internal pressure was held at 100 psi while the diameter of the tank was varied at 80, 

100, and 120 inches. The calculated force deflection curves for these different pressure tanks are 

shown in Figure 278. The comparison shows that the tank diameter has a very small influence on 

the tank stiffness under the side compression loading. 

Figure 278. The effects of tank radius on quasistatic compression loads. 

In the final series of analyses, the tank design was fixed (600 lb Cl tank) and initial internal 

pressures of 0, 50, 100, and 150 psi were analyzed. The calculated force deflection curves for 
217

these different pressure tanks are shown in Figure 279. The pressure has a large influence on the 

tank stiffness under the side compression loading. This is seen clearly by the comparison to the 

force-deflection behavior of the unpressurized tank. Without the pressure the force deflection 

curve is very nonlinear with reductions in the compaction stiffness at increased deflection levels. 

Figure 279. The effects of tank pressure on quasistatic compression loads. 

To quantify the effect of the internal pressure, we determined the relative stiffness of the various 

tanks between 8 and 10 inches of displacement. This is a portion of the response after the initial 

jacket compaction is complete and before the variable pressure effects become large. A plot of 

this effective tank stiffness against the tank pressure level is shown in Figure 280. A fit shows a 

relatively linear increase in the tank stiffness with the internal pressure levels. At 100 psi the 

compaction stiffness of the tank is nearly four times that of the unpressurized tank. 

Figure 280. The effects of tank pressure on quasistatic compression stiffness. 
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6.3.2 Side Impact Analysis Algorithm 

The approach used to develop a side impact analysis algorithm is to develop a spring-mass 

model for the tank that can replicate the force-deflection characteristics for side loading against 

various objects (e.g., impactor, reaction wall). These loads can then be applied with equations for 

the tank kinematics under the combined actions of the loads. 

The side impact algorithm was developed with Python coding language (van Rossum, 2012)

using the NumPy scientific computing package (NumPy, 2012). The equations of motion were 

written in matrix form as a series of first-order differential equations and integrated with a fixed 

time step. The objective is to fit the mode across multiple trials (impact conditions) and develop 

optimized spring constants & tank mass distribution. Wherever possible, information about the 

tank known physical behaviors are used as constraints. 

A schematic of the spring-mass system used for the side impact algorithm is shown in Figure 

281. The tank is represented by a series of five symmetric masses connected by springs. The 

outer masses (M1) are small and represent a small region of the tank that is involved with the 

initial interaction with the impactor or reaction structures. The secondary masses (M2) represent 

the region of the tank in the deformation zone around the impactor or reaction structures that 

become significant as the deformation progresses. The central mass (M3) is the remainder of the 

tank mass. 

Figure 281. Idealized schematic of the side impact spring mass model. 

The impact is modeled using a rigid impactor mass (MI) and an external nonlinear spring (KI) 

between the impactor and the outer tank mass on the impactor side. The impactor mass can be 

given different BCs such as a constant velocity or bee free to decelerate based on the interaction 

forces with the tank. The general characteristics of the external spring are a relatively low 

stiffness over the initial 4 inches of travel (the initial engagement and crushing of the jacket 

standoff) followed by a high stiffness spring. This effectively produces a constraint where the 

motions of the impactor and the outer mass under the impactor have equivalent displacements as 

long as the interaction force is compressive. 

The approach used for the reaction on the back side of the tank is similar to the approach used on 

the front side of the tank. The reaction mass (MR) can be given various displacement BCs (e.g., 

fixed or free to translate). For a stiff object, such as the reaction wall, the spring interacting with 
219

the external tank mass (M1) will be similar to the external impactor spring. This will allow for a 

small amount of tank displacement at low interaction forces while the standoff distance from the 

tank to the jacket is crushed. After the standoff is eliminated, the high external spring stiffness 

will effectively result in a displacement constraint against the reaction for the external tank mass. 

A significant difference of the reaction model is the addition of a secondary spring between the 

reaction mass and the secondary tank mass (M2) on the reaction side. This additional spring was 

necessary to model the interaction of a much larger contact area (such as the reaction wall). The 

properties of this secondary spring will be a function of the reaction wall size and if the reaction 

is localized to a small contact area this secondary spring is eliminated. 

Another physical characteristic of the impact response that was added to the spring-mass model 

is the effects of nonlinear elastic-plastic unloading behavior. When the forces between the tank 

and impactor (or reaction wall) begin to unload, they do not follow the initial loading curve. This 

is a result of the plastic deformations of the tank shell around the impact zone. The springs were 

modified to be elastic-plastic springs where they load along an initial linear path with the spring 

displacements divided into elastic and plastic components. When the interaction begins to 

unload, the unloading occurs with the elastic components of the displacement only. The model 

uses a ratio of 70 percent plastic and 30 percent elastic deformations during the loading process. 

A comparison of the idealized elastic-plastic spring behavior with a calculated force-deflection 

curve for an impact response with unloading is shown in Figure 282. The comparison shows that 

the 70 percent plasticity approximation is reasonable for the tank impact response. 

Figure 282. Idealized elastic-plastic spring behavior and calculated unloading response. 

The values used for the spring-mass model parameters were derived in a two-step fitting process. 

Initially, a series of Monte-Carlo analyses were performed where the parameters were allowed to 

vary randomly, within ranges determined by physical constraints. Results were compared to a 

series of FE impact analyses and the correlation for each set of parameters was determined. 

Subsequently, the parameters that provided the best fit to the impact data were optimized by 

finding the minimum error in the parameter space around the initial Monte Carlo parameter set. 

The values that were selected based on this methodology are summarized in Table 21. 

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A similar comparison of analyses with different BCs is shown in Figure 284. In this example, a 

series of 15 mph impacts were analyzed with the 9.55-in-diameter impactor and different 

restraint conditions on the far side of the tank. The BCs included both a free tank with no 

restraint conditions and tanks reacted by both a 25-foot-wide and 1-foot-wide reaction wall. The 

comparison shows that the spring-mass model does a good job of reproducing the variations in 

impact behaviors produced by different reaction BCs on the far side of the tank. 

Figure 284. Comparison of the FEA and impact algorithm for different BCs. 

The initial formulation of the spring mass system was developed for a center side impact 

scenario. However, the model can be easily modified to account for an off-center impact. The 

methodology for the offset impact scenario is illustrated in Figure 285. The local tank 

deformation and development of reaction forces are assumed to be identical to the center impact 

scenario. However, the tank motions relative to the impact point are now a combination of tank 

translation and rotation about the tank center of gravity (CG). Thus, the inertial characteristics of 

the tank are used to solve for the 2D tank motions and applied to determine the relative motions 

and dent depth at the impact point.

Using this methodology, a series of impacts was analyzed for the tank with a center impact and 

impacts with both 80-inch and 160-inch longitudinal offsets. The impactors used the 9.55-inchdiameter round impactor at a 15mph constant velocity impact condition. The tank was free to 

translate and rotate as a result of the impact forces. A comparison of the calculated behaviors 

with the FEA and spring-mass models for the three different impact conditions is shown in 

Figure 286. Again, the spring-mass model agrees well with the FEA predictions of the impact 

behaviors. 
222

Figure 285. Idealized schematic of the offset side impact model kinematics. 

Figure 286. Comparison of the FEA and impact algorithm for offset side impacts. 

A final comparison was made for the side impact analyses of a 500 Lb EO tank car at different 

impact speeds. In the above comparisons, the model was developed and optimized for the 600 lb 

chlorine tank car pressurized to 100 psi. For the EO tank car, the parameters were modified 

based on the results of analyses from Section 6.3.1. The larger radius of the tank does not 

significantly modify the algorithm, as shown in Figure 278. The tank shell thickness for the 500 

lb EO tank car is 0.918-inch and the corresponding thickness for the 600 LB chlorine tank car is 

0.981-inch. This results in a thickness correction in the tank stiffness of approximately 2 percent 

from Figure 277. Finally, the tank pressure of 50 psi for the EO tank car compared to the 100 psi 

for the chlorine tank car results in a reduction of the tank stiffness of 36 percent. As a result, all 
223

the spring stiffness values for the EO tank car were scaled to 63 percent of the original stiffness 

in the chlorine tank car model. The values for the masses were maintained from the chlorine tank 

model to the EO tank model. 

A comparison force deflection curves from detailed FE and simplified spring mass analyses of 

side impacts on an EO tank car at different impact speeds are provided in Figure 287. Overall, 

the agreement is quite good for model parameters scaled using this approximate methodology. 

This level of correlation would be suitable for many applications. However, if an improved fit is 

desired, a secondary optimization process could be performed for alternative tank car designs. 

Figure 287. Comparison of the FEA and impact algorithm for an EO tank car. 

6.4 Development of the Characteristic Puncture Force

The above sections describe analyses that can predict the force-deflection behaviors. However, 

the point along the force-deflection curve at which the tank is punctured also needs to be 

determined. This puncture force will be dependent on both tank geometry (materials and 

thicknesses) and the impact conditions (impactor size and impact orientation). 

Our approach to developing a tank puncture criterion for the tank impact algorithm(s) was to use 

puncture data from all the detailed FE puncture analyses described in this report and develop a 

“characteristic puncture force” parameter that is a function of the impactor characteristic size 

(defined in Section 3.2.2). A collection of the calculated puncture forces for various tank and 

impact conditions is shown in Figure 288. As expected, there is a general trend in the data with 

increasing puncture loads for increasing ram characteristic size. However, for any given ram 

characteristic size, there is a large spread in puncture forces. This is because the puncture force 

for an oblique impact against a 111A100W1 tank car will be much lower than the puncture force 

for a normal impact against a 105J600 tank car. 
224

Figure 288. Initial set of tank puncture forces under various impact conditions.

The first correction that can be made to the data is to correct for the tank design. Previous 

analyses of tank car puncture behavior have established that the puncture force for a given 

impact scenario scales approximately linearly with the combined thickness of the tank and 

jacket. This trend is consistent in the analyses performed in this study, as shown in Figure 289. 

The figure plots the puncture forces for the normal impact analyses with the different rectangular 

impactors and all the different tank cars analyzed in this study. The comparison shows that the 

puncture forces correlate well to a linear fit against the combined tank and jacket thickness. A 

similar correlation was also seen for the round impactor geometries. 

Figure 289. Effects of tank thickness on puncture force for various size impactors.

One potential modification to the thickness correction is to assess the puncture performance of 

the tank and jacket thickness independently. The assumed form of the thickness correction was:


227

Figure 292. Effects of impactor shape on puncture force in 45-degree oblique impacts.

Figure 293. Effects of impactor shape on puncture force in 30-degree oblique impacts.
228

Figure 294. Effects of impactor shape on puncture force in 15-degree oblique impacts.

Figure 295. Impactor shape corrected puncture forces for 45-degree oblique impacts.

A final correction factor observed for the oblique impacts is an effect of the impactor size. The 

angle correction factor, shown in Figure 291, were developed using the 12x12 inch square 

impactor. At this size, the 45-degree oblique impact puncture forces were reduced by 

approximately 60 percent. However, when a wider range of impactors are analyzed in oblique 

impacts, as shown in Figure 296, we see that the drop in puncture force is much less for small 

impactor sizes. 

230

Figure 297. Impactor size correction for oblique impact puncture forces.

Figure 298. Correlation of characteristic puncture forces for various impact conditions.
231

7. Analysis of Real-World Threats

7.1 Introduction and Background

The other chapters of this report are focused on the safety of tank cars in accidents and 

derailments. These events that occur as part of normal rail operations are the most common 

events that lead to releases of hazardous materials in rail operations. However, the security of 

tank car from an intentional attack is also a consideration for these designs. The Department of 

Homeland Security (DHS) has done several small- and full-scale tests of components and tank 

cars subjected to different acts of terrorism. The objective of the analyses described in this 

section is to assess the puncture performance in impacts (safety) of a protection concept 

developed by DHS for security against various threats. 

7.2 Protection System Design

The DHS, in collaboration with the Army Research Laboratory (ARL) evaluated a range of 

different tank car protection concepts against multiple security threats (Yen, Kaste, Montgomery, 

Cheeseman, & Scott, 2011). One of the best performing concepts, that also appeared to have 

potential for improving performance in accidents and derailments (safety applications) was the 

punched plate configuration illustrated in Figure 299. The system consists of two 1⁄4-inch-thick 

perforated panels made of High Hard Steel (HHS). The perforations were 3/8-inch diameter 

holes in a hexagonal pattern with 1⁄2-inch spacing between the nearest neighbor hole positions. 

The two panels are used in an offset configuration as illustrated in Figure 299(b). 

Material test data for the HHS was not made available for this study. Instead, DHS/ARL 

provided parameters for a simplified Johnson-Cook constitutive model in LS-DYNA (LSTC, 

2003) which they claimed was validated against test data (Jeong, et al., 2009) This validated 

constitutive model was used to simulate a tensile test which was used as the material “test” data 

to develop the constitutive and failure parameters that were used in the puncture analyses. The 

simulated tensile test behavior for the HHS is shown in Figure 300. The methodologies used to 

develop the constitutive and failure parameters were described in Section 2. 

The analyses of the HHS show that it has a very high yield strength compared to typical tank car 

structural materials. The yield strength for the HHS is approximately 230 ksi and the elongation 

calculated for the round bar tensile test was approximately 16 percent. The greatest uncertainty 

in the calculated tensile behavior is the elongation value which is sensitive to the specimen 

geometry and gauge length used in the test or analyses (a 2-inch gauge length was used for the 

analysis). A confirmation of the elongation for this configuration cannot be made without access 

to material test data. 

For analysis of the impact and puncture behavior of a tank with the punched plate protection 

system some additional model development was required. In the detailed impact zone, the 

geometry of the punched plates will be explicitly modeled. However, outside the impact zone, an 

effective material is needed that will have the equivalent stiffness and strength of the punched 

plates but can be modeled with larger shell elements. To create the “effective” material model we 

simulated a tensile test on a section of punched plate material. The simulation of the tensile test 

on the punched plate specimen is shown in Figure 301. The calculated engineering stress-strain 

curve for the punched plate tensile test is compared to that of the solid HHS material in Figure 

302. The comparison shows that the punched plate geometry both significantly reduces the 
232

stiffness and strength compared to the solid material. The effective elastic modulus is less than 

20 percent of that for the solid steel. The effective yield stress is reduced to approximately 40 ksi 

and the engineering ultimate stress for the punched plate material is approximately 65 ksi with an 

elongation of 20 percent. 

(a) Punched plate geometry

(b) layered punched plates

Figure 299. Configuration of the layered punched plate protection concept (Yen, Kaste, 

Montgomery, Cheeseman, & Scott, 2011). 
233

Figure 300. Simulated tensile test behavior for the High Hard Steel.

(a) Initial configuration

(b) Deformed specimen (before failure)

(c) Calculated failure mode

Figure 301. Simulated tensile behavior of the punched plate material.
234

Figure 302. Comparison of the solid and punched plate tensile behavior.

7.3 Side Impact Puncture Analyses

The side impact puncture analyses were performed for a 105J500 chlorine tank car protected 

with the punched plate system. The impact and puncture analyses use the methodologies 

described previously in Section 3 of this report. The model for a representative normal side 

impact analysis with the punched plate system is shown in Figure 303. The model has been 

reflected about the two symmetry planes used for the normal impacts. The detail of the impact 

patch shown in the figure illustrates the region of the impact patch where the punched plate 

geometry is explicitly modeled. Within that region, the model has a uniform mesh density with a 

characteristic element size of approximately 0.040 inches (1 mm), as shown in Figure 304. Each 

layer of the punched plate has 6 elements through the 0.25-inch-thickness. This results in 

elements with an approximate 1:1 aspect ratio. 

The puncture behavior of the tank with the punched plate protection system is shown in Figure 

305. The example shown is for the 6x6-inch square impactor at an impact speed of 20 mph. The 

puncture response is very similar to that of tank cars with more traditional jackets. The side of 

the tank and punched plate system are dented inward by the impact. At sufficiently large 

displacements and forces the impactor punctures the tank. 

More detailed images of the impact zone and damage development for the 6x6-inch impactor and 

the punched plate system are shown at corresponding times in Figure 306 and Figure 307. The 

images in Figure 306 show both the tank wall and punched plate layers and the images in Figure 

307 show only the punched plate layers. The comparison shows that the punched plate system is 

penetrated by the impactor prior to the failure of the tank wall. This is common of most tank 

designs that the jacket fails at a time before the tank wall. 
235

Figure 303. Model for the punched plate concept impact analyses.

Figure 304. Details of the model for the punched plate impact patch.
236

Figure 305. Impact and puncture of the 500 lb chlorine car and punched plate protection.
237

(a) Early impact (b) After jacket failure (c) tank puncture

Figure 306. Calculated tank impact damage and puncture initiation.

(a) Early impact (b) After jacket failure (c) tank puncture

Figure 307. Calculated punched plate impact damage and puncture behavior.

A summary of the side impact analyses performed for the 105J500 chlorine commodity tank 

protected by the punched plate concept is provided in Table 22. The table summarized the impact 

conditions and calculated puncture forces and energies for the analyses. A comparison of the 

puncture forces and puncture energies for the 500 lb tank with the punched plate protection are 

compared to those of traditional 500 lb and 600 lb tanks in Figure 308 and Figure 309, 

respectively. The comparisons are for normal side impacts using the full range of impactor sizes 

and shapes as described in Section 3.2.1. For the 600 lb tank car both the lower and higher 

impact speeds, discussed in Section 3.3 of this report, are included in this comparison. The 

impact velocities selected for the punched plate concept analyses are the same as the higher 

speed analyses of that section. 

The comparison of the puncture forces for the different tank car designs, shown in Figure 308, 

shows that the punched plate protection system increases the puncture forces over the 11-gauge 

jacket for the 500 lb commodity tank. However, the increase in puncture forces is approximately 

10 percent. The puncture forces for the 500 lb tank and punched plate system are still 
238

approximately 15 percent lower than those of the 600 lb commodity tank with the 11-gauge 

jacket. 

Table 22. Summary of side impact analyses for the 105J500 tank 

and punched plate concept

Calculation Tank 

Type

Tank 

Shell

Shell 

Jacket 

Impact 

Conditions

Internal 

Pressure

(psi)

Puncture 

Force (lbs)

Puncture 

Energy

(ft-lbs)

R91A 500 lb Cl 0.777 in

TC128B 

Punched 

Plate

20 mph

6”x6” ram 100 psi 9.530E+05 1.390E+06 

R91B 500 lb Cl 0.777 in

TC128B 

Punched 

Plate

30 mph

12”x12” ram 100 psi 1.848E+06 4.260E+06 

R91C 500 lb Cl 0.777 in

TC128B 

Punched 

Plate

25 mph

9”x9” ram 100 psi 1.402E+06 2.770E+06 

R91D 500 lb Cl 0.777 in

TC128B 

Punched 

Plate

15 mph

3”x3” ram 100 psi 4.910E+05 3.260E+05 

R91E 500 lb Cl 0.777 in

TC128B 

Punched 

Plate

15 mph

3”x6” ram 100 psi 8.090E+05 9.770E+05 

R91F 500 lb Cl 0.777 in

TC128B 

Punched 

Plate

25 mph

3”x12” ram 100 psi 1.199E+06 2.130E+06 

R91G 500 lb Cl 0.777 in

TC128B 

Punched 

Plate

20 mph

5.73 in. dia. 100 psi 8.350E+05 8.600E+05 

R91H 500 lb Cl 0.777 in

TC128B 

Punched 

Plate

20 mph

7.64 in. dia. 100 psi 1.125E+06 1.820E+06 

R91I 500 lb Cl 0.777 in

TC128B 

Punched 

Plate

25 mph

9.55 in. dia. 100 psi 1.318E+06 2.720E+06 

R91J 500 lb Cl 0.777 in

TC128B 

Punched 

Plate

30 mph

11.46 in. dia. 100 psi 1.535E+06 3.110E+06 

R91K 500 lb Cl 0.777 in

TC128B 

Punched 

Plate

35 mph

13.37 in. dia. 100 psi 1.725E+06 3.400E+06 

The comparison of the puncture energies for the different tank car designs, shown in Figure 309, 

shows that the punched plate protection system is again closer to those of the 500 lb chlorine 

tank car than the 600 lb tank car. This result is roughly consistent with the amount of steel added 

to the various systems. The pinched plate geometry removes roughly 50 percent of the steel in 

each plate. Thus, the total system is roughly equivalent in weight to a monolithic 0.25-inch-thick 

steel jacket. Thus, the punched plate system adds only 0.13 inches to the effective jacket and 

tank combined thickness. By comparison the increase from the 500 lb to the 600 lb commodity 

tank adds 0.204 inches to the tank thickness. 

This comparison shows that the punched plate system is reasonably effective for tank car safety 

applications. It does not result in significant improvements in puncture resistance, but the 

performance is consistent with the modest levels of added weight for the concept. None of the 

analyses indicate that the punched plate protection system would introduce new damage modes 

that could result in reductions in the tank puncture resistance. 
239

Figure 308. Comparison of side impact puncture forces for different tank designs.

Figure 309. Comparison of side impact puncture energies for different tank designs.

To evaluate the effectiveness of the punched plate at increasing the tank resistance, additional 

analyses were performed where the punched plate system was replaced by 1⁄4-inch jackets that 

have roughly equivalent weight. The jacket materials considered were TC128B and HHS. A 

comparison of the 6x6 inch square impactor force-deflection behavior for these two jacket 

designs with those of the baseline 11-gauge jacket and the punched plate system is shown in 

Figure 310. The comparison shows that the punched plate system has a higher puncture energy 

than the 1⁄4-inch TC128B jacket but a lower puncture energy than the monolithic 1⁄4-inch HHS 

jacket. 
240

Figure 310. Comparison of side impact puncture energies for different tank designs.
241

8. Conclusions 

This report describes a research program to improve the safety and security of railroad tank cars. 

The approach used in the research and development program was to apply a tank impact and 

puncture prediction capability using detailed finite element analyses. The capability was 

developed and validated previously in the NGRTC program. In this study, the analyses were 

applied to investigate the tank puncture behaviors for a wide range of impact conditions. 

In the initial phase of this program, different size and shape impactors were investigated. A new 

parameter was developed to characterize the effective size of the impactor. This impactor 

characteristic size is the square root of the area of the impactor face. The impactor characteristic 

size parameter provides a good correlation for the different impactor sizes and shapes analyzed 

and is a useful parameter for quantifying the puncture potential for various impactors. For 

example, a rail section impactor has a characteristic size of approximately 5 inches. 

Alternatively, a more complex impactor, such as a coupler head can be assessed. Here the 

behavior is complicated by an impactor face profile that is not flat. As a result, the puncture force 

can vary significantly with relatively small changes in the orientation of the impact. For a limited 

set of impact orientations analyzed, the coupler head was found to have a characteristic size as 

small as 5 inches and as large as 12 inches. 

Two different series of analyses were performed to investigate the effects of the impactor 

orientation. The first series of analyses rotated the impactor orientation and maintained the 

normal impact trajectory. The second series of analyses used an oblique impact configuration. 

Both sets of analyses found that the rotation of the impactor face relative to the tank surface 

results in load concentrations at the edge of the impactor and significant reductions in the 

puncture force. As a result, the characteristic size of the 12x12 impactor drops from 12 inches in 

the normal impact to approximately 4.5-5 inches in an edge impact. The characteristic size is 

further reduced to approximately 3 inches for the corner impact. These results show that 

impacting objects with corners and edges can have the penetration potential of a much smaller 

object if the orientation of the impactor concentrates the loading to the edge or corner. 

A series of analyses were performed to investigate the effects of the constraint level on the tank 

side impact response. The analysis of the different tank boundary constraints shows that the 

effects on the late time behavior and puncture energy can be significant. However, the initial 

portion of the loading is dominated by the inertial resistance of the tank and the puncture will 

occur in this initial phase of the impact for many combinations of impactor sizes and impact 

speeds. Thus, for many side impacts, the constraint on the back side of the tank is not significant. 

A corresponding series of analyses were performed to investigate the effects of the constraint 

level on the tank head impact response. The constraint conditions were found to be more 

significant for head impacts. The tank constraint effects for head impacts are observed much 

earlier in the response than for side impacts for two reasons. The first is that the tank cylinder is 

much stiffer in axial loading compared to lateral loading. Thus, the head impact forces are very 

rapidly transmitted to translations of the tank center of gravity (CG). The second reason for 

increased constraint effects in head impacts is the behavior of the lading in head impacts. During 

the duration of the impact, only a fraction of the total lading mass is coupled to the motions of 

the unconstrained tank. Analyses to quantify the lading effect show that less than 10 percent of 

the lading is coupled to the motion of the tank for a typical head impact scenario. 
242

A set of analyses was performed to assess the effects of the temperature of the tank and lading 

for a chlorine tank car. As the equilibrium temperature of the tank rises, the vapor pressure 

increases, and the liquid density is reduced. A decrease in the liquid density will produce an 

increase in the liquid volume with a corresponding reduction in the outage volume. Both 

increasing the pressure and reducing the outage can reduce the puncture resistance of a tank car. 

The condition analyzed is a 105J600W chlorine tank car at an equilibrium temperature of 105o F. 

This temperature increases the internal vapor pressure for the tank to 155 psi and lowers the 

corresponding outage volume for a tank loaded to the specified limit to 7.5 percent. These are 

compared to the 100-psi internal pressure and outage volume of 10.6 percent at a tank 

temperature of 78 degrees F. On average, the increase in temperature dropped the puncture 

energies by 20 percent. However, the puncture energies for smaller impactor sizes are more 

similar at the two temperatures. This is because the impact response for small impactors is 

dominated more by the structural stiffness. The internal pressure (and pressure increase) plays a 

smaller roll for the small dent sizes from small impactors prior to puncture.

In addition to the analyses performed on the 105J600 tank car, a series of other tank car types 

were analyzed. The evaluations of TIH pressure tank cars were performed for the 500 lb chlorine 

tank car, the 340 and 500 lb AA tank cars, and 300, 400, and 500 lb EO tank cars. In addition, 

evaluations of various general purpose tank cars and DOT-113 LNG tank car designs were also 

evaluated. For the side impact evaluations, a full set of normal and 45-degree oblique side 

impacts were performed for each of the tank car designs considered. For the head impact 

evaluations, offset impacts using various size square impactors was used. For comparison of the 

various designs, we normalized the calculated puncture energies from all the various designs 

against an appropriate reference tank car. 

In the comparison of TIH pressure tank cars, the side impact puncture energies for the 105J500W 

EO tank car are considerably higher than for any of the other tank car designs. The EO tanks 

have relatively high puncture energies as a result of the lower tank pressures and larger diameter 

tanks. The 105J500W, 105J400W, and 105J300W EO tank cars have puncture energies on 

average 82 percent higher, 17 percent higher, and 12 percent lower, respectively, than the 

105J500W chlorine tank car. The puncture energies for the 105J600W chlorine tank car were on 

average 37 percent higher than the 105J500W chlorine tank car. The 112J500W and 112J340W 

AA tank cars are on average 10 percent above and 39 percent below the 105J500W chlorine tank 

car, respectively. 

The head impact puncture energies for the TIH pressure tank cars show different trends in the 

puncture resistance. Due to the doubly curved geometry, the structural stiffness and tank 

thickness plays a larger role in the behavior and the internal pressure levels plays a lesser role in 

the impact energy dissipation. The head impact puncture energies for the 105J600W chlorine 

tank car were highest and, on average, 28 percent higher than the 105J500W chlorine tank car. 

The 105J500W, 105J400W, and 105J300W EO tank heads have puncture energies on average 22 

percent higher, 10 percent higher, and 18 percent lower, respectively, than the 105J500W 

chlorine tank head. The 112J500W and 112J340W AA tank heads are on average 3 percent

above and 34 percent below the 105J500W chlorine tank head, respectively. 

The analyses of the side impacts for the DOT-111 class of general-purpose tank cars investigated 

a range of tank designs and design concepts. The P1577/CPC 1230 tank car (0.50-inch-thick 

TC128B tank shell) with a jacket and head shield provided an approximately 40 percent increase 

in average puncture energy over a DOT-111A100W1 tank car when the worst-case outage 
243

volume of 1 percent is applied. When the outage volume is increased to 3 percent, the jacketed 

P1577/CPC 1230 tank car provided an approximately 120 percent increase in average puncture 

energy over a DOT-111A100W1 tank car. In head impacts, the P1577/CPC 1230 tank head with 

a head shield provided an approximately 80 percent increase in average puncture energy over the 

DOT-111A100W1 tank head. Similarly, the DOT-117A100W tank head (with a head shield) 

provided an approximately 95 percent increase in average puncture energy over the DOT111A100W1 tank head (or 8 percent increase over the P1577/CPC 1230 tank head with a head 

shield). Although the DOT-117A100W tank car was not evaluated for side impacts, we would 

expect similar increases in the side impact puncture resistance over the jacketed P1577/CPC 

1230 tank car design. 

The DOT-113C120W9 LNG tank cars were found to have very good side impact puncture 

resistance. The average puncture energy for the DOT-113C120W9 tank car is 126 percent higher 

than the DOT-105J500W chlorine tank car. In addition, the average puncture energy for the 

DOT-113C120W9 tank car is higher than those of all the TIH pressure tank car designs 

analyzed. Additionally, the average puncture energy for the DOT-113C120W9 tank car is 8.46 

times higher than that of the DOT-111A100W1 tank car and much higher than those of all the 

general-purpose tank car designs analyzed. An evaluation was also performed for a modified 

DOT-113 tank design with a 0.50-inch-thick tank shell meeting the requirements of the AAR 

Specification M-1004 for LNG fuel tenders. This M-1004 compliant DOT-113 tank car was 

found to have an additional 44 percent increase in average side impact puncture resistance over 

the baseline DOT-113 tank design. 

The DOT-113C120W9 LNG tank again was found to have very good head impact puncture 

resistance. The average puncture energy for the DOT-113C120W9 tank head is 127 percent

higher than the DOT-105J500W chlorine tank car and higher than those of all the TIH pressure 

tank car designs that have been analyzed. This M-1004 compliant DOT-113 tank head was found 

to have an additional 45 percent increase in average head impact puncture resistance over the 

baseline DOT-113 tank head design.

The FE modeling approach used for all the above impact analyses is very useful for 

understanding the mechanics of tank impacts and punctures. However, at times, a simplified 

analysis methodology or impact algorithm is useful for the assessment of various factors on tank 

impact safety. In this study, we developed analytical tank impact algorithms that can be applied 

for future analyses of tank car safety. When assessing appropriate analysis methodologies, we 

examined the response characteristics of both head and side impacts. We found that the 

behaviors for these two impact conditions are sufficiently unique that different analysis 

methodologies were appropriate for the head and side impacts. The resulting models were 

compared to the FE analyses of different impact conditions and found to provide good 

correlation to the FE results. 
244

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Appendix A. 

Tank Head Puncture Resistance Performance Standards

49 CFR § 179.16

Tank-head puncture-resistance systems.

(a) Performance standard. When the regulations in this subchapter require a tank-head 

puncture-resistance system, the system shall be capable of sustaining, without any loss of lading, 

coupler-to-tank-head impacts at relative car speeds of 29 km/hour (18 mph) when:

(1) The weight of the impact car is at least 119,295 kg (263,000 pounds);

(2) The impacted tank car is coupled to one or more backup cars that have a total weight of at 

least 217,724 kg (480,000 pounds) and the hand brake is applied on the last “backup” car; and

(3) The impacted tank car is pressurized to at least 6.9 Bar (100 psig).

(b) Verification by testing. Compliance with the requirements of paragraph (a) of this section 

shall be verified by full-scale testing according to appendix A of this part.

Appendix A to Part 179—Procedures for Tank-Head Puncture-Resistance Test

1. This test procedure is designed to verify the integrity of new or untried tank-head punctureresistance systems and to test for system survivability after coupler-to-tank-head impacts at 

relative speeds of 29 km/hour (18 mph). Tank-head puncture-resistance is a function of one 

or more of the following: Head thickness, jacket thickness, insulation thickness, and material 

of construction.

2. Tank-head puncture-resistance test. A tank-head puncture-resistance system must be 

tested under the following conditions:

a. The ram car used must weigh at least 119,295 kg (263,000 pounds), be equipped with a 

coupler, and duplicate the condition of a conventional draft sill including the draft yoke 

and draft gear. The coupler must protrude from the end of the ram car so that it is the 

leading location of perpendicular contact with the impacted test car.

b. The impacted test car must be loaded with water at six percent outage with internal 

pressure of at least 6.9 Bar (100 psig) and coupled to one or more “backup” cars which 

have a total weight of 217,724 kg (480,000 pounds) with hand brakes applied on the last 

“backup” car.

c. At least two separate tests must be conducted with the coupler on the vertical centerline 

of the ram car. One test must be conducted with the coupler at a height of 53.3 cm (21 

inches), plus-or-minus 2.5 cm (1 inch), above the top of the sill; the other test must be 

conducted with the coupler height at 79 cm (31 inches), plus-or-minus 2.5 cm (1 inch), 

above the top of the sill. If the combined thickness of the tank head and any additional 

shielding material is less than the combined thickness on the vertical centerline of the car, 

a third test must be conducted with the coupler positioned so as to strike the thinnest 

point of the tank head.
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3. One of the following test conditions must be applied:

Minimum weight of attached 

ram cars in kg (pounds)

Minimum velocity of 

impact in km/hour (mph) Restrictions

119,295 (263,000) 29 (18) One ram car only.

155,582 (343,000) 25.5 (16) One ram car or one car plus 

one rigidly attached car.

311,164 (686,000) 22.5 (14) One ram car plus one or more 

rigidly attached cars.

4. A test is successful if there is no visible leak from the standing tank car for at least one hour 

after impact.
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Abbreviations and Acronyms 

ACRONYM DEFINITION

1D One Dimensional

AA Anhydrous Ammonia

AAR Association of American Railroads

ALE Arbitrary Lagrangian Eulerian

API American Petroleum Institute

ARL Army Research Laboratory

ATCCRP Advanced Tank Car Cooperative Research Program

BC Boundary Condition

BW Bao-Wierzbicki

CG Center of Gravity

DHS Department of Homeland Security

DOT Department of Transportation

EO Ethylene Oxide

EPFM Elastic-Plastic Fracture Mechanics

FE Finite Element 

FEA Finite Element Analysis

FRA Federal Railroad Administration

FMVSS Federal Motor Vehicle Safety Standards

GN2 Gaseous Nitrogen

HHS High Hard Steel

LEFM Linear Elastic Fracture Mechanics

LFM Local Fracture Mechanics

LN2 Liquid Nitrogen

LNG Liquid Natural Gas

NGRTC Next Generation Railroad Tank Car 

PHMSA Pipeline and Hazardous Materials Safety Administration

RAIRS Railroad Accident and Incident Reporting System

RFA Renewable Fuels Association

SPH Smoothed Particle Hydrodynamics
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ACRONYM DEFINITION

SS Stainless Steel

TC Transport Canada

TIH Toxic Inhalation Hazard

TCC Tank Car Committee

TTCI Transportation Technology Center, Inc.

TWP Technical White Papers